I know that the label Nintendo Selects / Player’s Choice is applied to games that have sold more than one million copies and are sold for less, but do they ever have content differences such as more or fewer levels or characters, different graphics/sprites, bug-fixes, etc.?
As far as content is concerned, no. You're getting the same game that the previous buyers got, it's just a different box.
While there may sometimes be bugfixes, there does not have to be. Any bugfixes introduced in the Nintendo Selects version are necessarily minor, and would not affect normal gameplay. This is necessarily the case because there is no patching mechanism for the already released copies; if there are major bugs which severly impact the gameplay (such as the freezing bug in PAL copies of Super Paper Mario), the only way to fix them is by replacing the disc or cartridge.
Additionally, any bug fixes are not made specifically for the Nintendo Selects version, and may have already been released in previous pressings. Whether or not the two coincide is a question of when they switched the master copy; that may happen at the same time as pressing additional copies for the Nintendo Selects version, or it may not.
TL;DR: There are no notable differences.
Besides the box, I believe I've seen the sticker art looking different (including a Players' Select badge). For instance, This forum post shows some pictures of multiple versions.
There can be differences in releases even when you're not dealing with the "Player's Select" marketing-based cosmetic update.
For instance, in The Legend of Zelda for the NES, Nintendo made some improvement(s) to help reduce the chances of saved games being deleted. Along with that, they altered the message about needing to hold down the RESET button. (Actually, as I understand it, the very earliest cartridges didn't even have such a message. Then they added it. Then they removed it.)
Other changes can also exist. For instance, using the same game, see: The Cutting Room Floor: The Legend of Zelda. That website has details about different variations of many games.
All in all, such changes do tend to be very minor, such as bug fixes. You don't tend to get different bosses, additional dungeons, etc. The couple of cases (that I can quickly think of off the top of my head), Nintendo makes that abundantly clear in the marketing. In fact, they change the game's title. "Mike Tyson's Punch Out!!" became "Punch Out!!", and "The Legend of Zelda: Link's Awakening" became "The Legend of Zelda: Link's Awakening DX".
What I expect Nintendo's typical process is, for making a Player's Select release, is they simply use whatever software version is the latest already-created version. I'm not aware of any examples of that not being true, nor do I know why they would do so. However, if they did decide to adjust the content to include a new "Player's Choice"/"Player's Select" badge, I would expect them to increase the latest year shown on the copyright date, and I would expect "The Cutting Room Floor" website (as mentioned earlier) to quickly have those details.