Actually mask of madness is great on her. The primary thing about a MoM is that it's a farm accelerant - it makes you farm faster. If you're going to be "up to par" in power as a carry, you have to get some sort of item that speeds up how quickly you get gold. (Either that, or your teammates have to foie gras you with kills, which is wishful thinking against any opponents that are as good as you are - it happens on a lucky day, but it's not a reliable way to win.)
This principle is why you would always go MoM -> Skadi, and never Skadi -> MoM; if you do it in the first order, you'll finish both in half the time as the second order.
Spectre's weird because she's not really an illusion hero like the other illusion heroes. She has an ability that creates illusions, yes ... but as a tool for straight up fighting it's terrible compared to other illusion heroes. It's on an enormous 120sec cooldown, lasts for only 5-7 seconds, and creates (dmg out/in) 30%/200% illusions. Compared to Naga with a 40sec cooldown, lasts for 30 seconds, and 35%/300%.
The best way to express why spectre isn't an illusion hero is to describe it in terms of uptime - Naga's illusions are active 75% of the time (and even 100%, if she's got an Octarine). Terrorblade's illusions can be active 100% of the time. PL's illusions are active 100% of the time (as long as he's fighting something). Spectre's illusions are active about 5% of the time, and then they go on that brutal 120sec cooldown for the other 95%.
The trick to understanding spectre is that her ult isn't to fight with; instead, it's a global teleport, a global invis-and-smoke-piercing enemy-position-reveal, and an escape/confusion technique - you use it to:
- find out where everyone on the enemy team is, typically to pick a target who's vulnerable to being killed (but this can also save your life if triggering your ult reveals that the whole enemy team is near enough to respond). This information pierces invis and smoke - even if you can't see them, the illusion will appear next to them, so with some dust this can be great against e.g. Riki.
- teleport in to save an ally (conveniently this is also a point in time where it's unusually valuable to get info about the enemy team's position, because ganks often move in groups - spectre's ult can reveal that the one person jumping your teammate was actually several people). There's also strong synergy on this with spectre because against some lone gankers, your
Desolate passive kicks in, and their disables are probably on cooldown.
- confuse the enemy during a large teamfight by spawning some fairly tanky illusions (only 200% more damage taken than the real spectre), of which any one could be the real one. These illusions last a very short time, so the right-click damage and radiance damage that they deal (even optimized for effects that have full power on illusions) is kind of a joke. The real point of them is to last long enough (and seem durable enough) that the enemy has a hard time figuring out if they are, in fact, the real one - to buy you time.
- via the above confusion, to escape. A very common trick as spectre is to use the ult to swap towards some distant member of the enemy team that doesn't have killing potential against you, and then to dagger away to safety.
So it doesn't matter that battle-fury (or anything!) doesn't work on illusions.
Battle Fury Battle Fury's not bad on her - it's not great either, but it actually it has become better in the new meta of 6.85 (due to the +20% creep damage and the built-in quelling blade); the big knocks against it are that her raw physical damage is moderately low compared to other "traditional" battle-fury carries who, in addition to being agility characters, have some unusual trait that boosts their raw attack damage. These are crits on jugg and PA - remember that crits do spill into cleave damage, and a high BAT on jugg and AM. Faceless Void actually has no unusual character traits to recommend Battle Fury on him (his time-lock damage does NOT cleave) - his only oddness is he'll often find himself fighting grouped enemies in his ult. The other big knock against it on spectre is that her desolate passive (which does not cleave) turns off when she's fighting multiple enemies (creeps or heroes), which usually is an incentive for her to stop fighting - however, this is also a weird plus for it; if the thing turning off her passive is a creep wave, she'll kill the creeps a lot faster with battle-fury than with a radiance - she can keep hitting the enemy hero and the creeps will all die in a few strikes, re-exposing the hero to desolate.
Radiance The big sell for radiance on her is that it makes her (and her whole team) tankier via evasion, and disables blink daggers. The thing with blink daggers is that if spectre's going in against a single target (like a lion off warding or killing a few lane creeps), usually what happens is that they'll freak out for a moment, and defensively stun you... for about as long as it takes to re-enable a blink dagger. Radiance keeps the blink dagger off, and because spectre's so tanky, and so insanely fast with her dagger (a 40% speed differential, since it's a slow and haste), you can usually shrug off the stun/nuke and chase such a hero - as long as they don't blink away. It also makes her farm a good bit faster against lane creeps, but it's somewhat poor against most jungle creeps. Lastly it puts heavy tactical pressure on the enemy - once you have radiance they can no longer have indecisive dance-and-dodge fights where neither team fully engages; any time when they're near you, they're taking a lot of damage.
The big danger with radiance is it doesn't scale. You get 50dmg/sec and that's it. It's an snowball item meant to put your opponents in a sort of choke-hold; it's built to put enemies with low HP and low regen/lifesteal in a vicious cycle where they can't engage you without dying (and then your team can knock over all the objectives and win). A lot of times, supports (and some agility carries) won't buy hitpoint items, but if they do, and if they've got decent lifesteal (or a pipe), that radiance you've spent half the game farming can be countered, and once its countered, it's not an item that has a lot of synergy with other builds. Try to avoid building it against strength carries, or against opponents that are snowballing too quickly and are already well on their way to building the counters to it.
Mask of Madness This is actually crazy-good on her, provided you're not dumb and activate the item when a powerful enemy nuke is ready. It synergizes very well with all of spectre's natural traits - her Dispersion passive dramatically lowers the vulnerability MoM usually gives you, and increasing her attack speed doubles the number of procs of Desolate, vastly increasing her damage.
More importantly, with the 6.85 buff allowing Desolate to work on jungle creeps, this allows spectre to jungle very, very quickly, and sustains her health whilst jungling. (Her mana can generally handle the load just fine, and if not, something dirt cheap like basilius can shoulder the load). The reason it's so good is that it provides a huge boost to your farming speed (like BF or Radiance) in a tiny fraction of the cost (1800 gold). It also lets her move between camps more quickly, which radiance and battle-fury don't.
Because it's so cheap, it comes online very quickly (ideally right after laning), and is cheap enough that retiring it later when you're ~5 slotted isn't a hard choice nor a financial setback.
Maelstrom The only other option to damage multiple creeps is Maelstrom. Maelstrom does nothing to replenish mana/hp, but it does have a markedly faster buildup than radiance/battlefury. It also builds into Mjolnir, which is good on spectre because Desolate benefits heavily from attack speed, and because Mjolnir's active also works well on her as a means of managing enemy aggro.
Midas The only real selling point of midas, for any hero, is that it gives XP (for heroes who get unusually high impact from higher-level abilities, i.e. invoker), and that it's the only thing in the game that gives reliable gold for killing creeps. The reliable gold means that Midas is much more of an important item if you're in a difficult game where you're dying a lot, and your whole team has lost map control - it's a very mediocre item to buy in a game where you're doing reasonably well and you've got space to farm, because it farms more slowly than other items. Midas can turn around games that have otherwise already been lost, but unless you need the XP, you're probably better off with a regular BF/Maelstrom/etc.
