As already mentioned while exploring the world and jumping here, rock climbing there, they have issues to follow you, not to mention most have stealth problems. Also most of them seem to be stucked on a fix level when you meet them (PC users can "fix" this with console commands, but there will be often multiple default gear which you have to delete as well).
Also the folloers equip system is plain stupid. While neclases and rings are not a problem everything else is. Often they equip only "highest armor rating wins" that means you never are able to swap a mages default robe by for example the archmage robe because both share armor rating of zero. Also most of the followers with high one-handed combat wont use dual-wield (someone mentioned one that I didnt try up to know). Not to mention they wont recharge their weapons even with soul gems, etc.
Beside the stats or looks of followers, if you really want to use one for long time I recomment an archer or mage type. So far I had good experience with "Aranea Ienith" (Azura Star quest) because she summons flame atronachrs and uses long range spells. Also any hunter should work, Aela did their job pretty well.
I made the experience if they some place their fighting AI is pretty good. Means they do their best outdoor. They hide behinde rocks if necessary, hit on long distance and other stuff.
Anyone know if the dismiss bugs been fixed for Illia yet?
As far as I know it isnt, also it seems that enable/disable console commands wont help either