I have had many of these same issues:
1. Keypresses randomly registering outside of osu mid song (particularly bad in mania)
2. When attempting to load a new map, it just infinitely loads and I have to manually delete the map from within osu to be able to play again
3. Random crashes on song select
4. Pretty severe input lag
5. Certain maps having wrong thumbnail or wrong C/B/A/S/SS ranks associated with them at select
6. The worst of them all, after updating from within client, the entire game gets broken with the .NET framework error and must be redownloaded
I've found a fix for #2 however, the issue is caused by a certain number of maps being skeletons (that is to say that they have a folder within the game, and they have a .mp3 and a background, but no .osu beatmap file). One of the ways that skeletons get created is by choosing the "Delete all visible beatmaps" at song select, but I'm sure there are others. Choosing this option will create skeletons of all the maps that you want to delete (I'm pretty sure other deletion options are fine). If you have a certain number of skeletons, new maps will not load. Here's how get rid of skeletons:
1. hit f5 at song select
2. If the song that starts playing mysteriously does not have a beatmap associated with it, then you have a skeleton
3. look at the name of the song playing in the top right corner of the main title screen, the song name should be the name of the .mp3 in the skeleton, this will help you find it
4. Go to your appilcations, right click on osu, click "Show Package Contents" then navigate to your songs folder and search for that .mp3 file's name
5. Once you find the beatmap, double check to make sure it's a skeleton (no .osu file inside) then manually delete
6. Hit f5 again to repeat
I once had to delete 50+ skeletons, not fun. Hopefully this will help some people and hold them over until lazer. (But seriously fuck the .NET framework init error, 4th time having to redownload this game)