The Fediverse lacks some sort of “shared”, agreed-upon identity and some “structure” of whichever sort to communicate that identity to the “outside” world. This causes interesting and at times annoying effects, because that's very much unlike what Mastodon gGmbH does - they do marketing, communication, advertisement in this way or the other which might be a reason for Mastodon (as a brand/software name) being quite a bit more known than Fediverse (as a much more vague term for a distributed communication network). There would be an obvious solution to that problem but in most cases this seems to be addressed or resolved by blaming Mastodon for how they handle things. Which is at least disputable.

The Fediverse is driven by enthusiasts and most of them are very passionate about what they do. That's a good thing if you manage to chime in and let their enthusiasm come for you. It's slightly more difficult in some cases if requests, needs, reports seem to get into way of this enthusiasm. The best thing is not to be heard, seen, taken seriously. There are worse outcomes which I don't want to quote here in detail but cause me, in example, to stay away from Loops or Pixelfed for an indefinite period of time no matter how good they might eventually get.

Community-wise, depending on where you pop up and how you get started, Fediverse itself can be overwhelming and also somewhat unwelcoming. This has improved a bit recently per my perception, but, more or less unconsciously touching the right topics one can end up in nasty disputes all along even ones very first posts out there. From that point of view it somehow sometimes resembles strictly maintained late-1990s mailing lists where you could expect a strong lecture on your mistakes much more than people being mellow or forgiving with those who are new to the party.

There's a fuzzy line between “an instance” as a server of some sort to provide access to the Fediverse and “an instance” as a place for a certain community to hang out. In most of these cases, people to technically run infrastructure are the same who have community moderation responsibilities, and not in all cases (omg.lol being a good exception from that rule again) there's a real team, crowd, organized process on how moderation or community management happens. Likewise, there seem to be admins and moderators considering themselves essentially servants of their respective communities, and there are those who consider the server they run to be, in the end, their living room, their private garden, … where, all else aside, it's essentially them and only them to make the rules. Nothing wrong with that in general, but that might cause an interesting amount of friction one doesn't really want or like or need.