Depending on the server configuration, installed modifications, and how things are setup there can be a large number of different issues. Or if you're lucky (no modifications installed, etc) none at all.
When a forum is several versions behind I usually suggest trying the upgrade on a test copy in order to see how it goes, and eventually fix any bugs you encounter so that you're ready for upgrading the live site with no surprises.
Another thing would be checking which modifications and custom themes you use (if any) and see if there are updated versions of them for the suite version you're going to upgrade to. For example if a modification critical to keep your forum working is not updated you'd have to first reach out to its developer and see if they can update it. If they're not available you may need to update it yourself (if you know how) or you may need to hire a different developer to update it for you. There could also be modifications that aren't updated but that you don't mind losing either. Some modifications might still work without changes, but themes surely won't since they won't support all the new features IPS added.
As an example I recently upgraded a client's forum from 4.2 and beforehand I updated 3 custom modifications for them since the original developer wasn't available anymore. We also did a test upgrade and found some columns from old uninstalled modifications that caused errors during the upgrade process. Thanks to that we fixed the live site's database and ended up avoiding the error completely.
As I mentioned above anything can happen and there isn't really a list that covers known issues: the best way would be to compile your own list by making a test upgrade and seeing what happens directly.