There are some emblems for sale, by Speaker and by factions. Do they have some hidden buffs? Do faction emblems give some reputation gain bonus?
Event emblems (The Queen's Wrath and Iron Banner) give 10% reputation gain bonus for event activities.
All others do not have any bonuses, they're just for show.
Faction emblems do not increase rep gain. I did some tests and with nightfall bonus bounties still give +62 and +125 rep (50 and 100 plus 25% from nightfall) even with both faction emblem and banner equiped.
I did not find any bonuses in Speaker emblems too. There were some rumors for hidden buffs (on Destiny forums and Gamefaqs), but in my tests I did not find any effects described. I did not try all of them though, only several.
Another source - Planet Destiny:
We have off the record Bungie confirmation that emblems do not have any hidden buffs or bonuses of any kind.