when i watch a cover - full band, solo instrument, singing, whatever - i just like to see an understanding of the music they're playing.
there are several types of covers, and i think each one needs to be addressed individually.
those "covers" that sing the lyrics and melody over a stock I vi VI V that has nothing to do with the song usually make me mad as there was no attempt to learn the song at all. (sometimes these are done on purpose and work!).
it also matters if the person says specifically "this is note for note!" when it's not, i wonder if they actually think they're playing it note for note, or if they just say it so people think it is. many times people think they are hitting everything, when they actually aren't, and i think it's a disservice to any performer to just say "good job" and not let them know they aren't actually doing what they think they're doing. i've seen covers of meshuggah songs on drums, and they're really not hitting things and clearly have no understanding of the odd times. props for trying it of course, but i mean if you're not doing it, you're not doing it. and that should be shared with the person i feel, not in a threatening way of course. but the moment you do that, people start asking for proof that YOU can play it, etc etc... it's tiresome. so i rarely comment. people can post whatever they want, but they should know they open themselves up to comments and discussion about what they presented.
then there are re-interpreted covers that change things purposefully - sometimes small changes, sometimes major. i enjoy these the most and usually how i approach covers too. music is open for interpretation and i enjoy the creativity realized when having a starting point of a song that already exists. it's puzzling to me to see people say "you're not allowed to change that chord/note." however, sometimes the change is not a good choice or even technically bad/wrong, and those probably come from inexperience. so those i can't agree with.
again for me, it's about the understanding of the song. to not play a m7b5 chord in a song that uses and needs it because you don't know that chord exists is one thing - we all need to learn bit by bit, and playing a minor chord there instead doesn't sound quite right. but i can usually see that maybe the person doesn't know how to play that chord and typically excuse it. but if someone replaces that m7b5 chord with like a II7 or something that doesn't fit at all... yeah that's rough. i would view that as not understanding the song, and maybe it shouldn't be performed until you take the time to get the right chord.
if i see someone who isn't a "shredder" but their band on a weekend gig plays a song with a shreddy solo, but plays something slower that they can actually play, i wouldn't think "omg this guy sucks!" i would appreciate what they can perform and move on in life. i'm pretty sure they would love to play it as recorded, and are probably working on it week after week until they feel comfortable enough to try it.
so many casual listeners have no idea how much work it takes to become good at an instrument, and think because we have a guitar, we can immediately do anything the guitar gods can, and if we can't, we suck. that's why i try to assess what the musician is capable of in general, and appreciate it for what they give to the listeners. clearly some people are just bad musicians and truly need to practice more, but i'd rather see an honest performance of them giving their energy to the room vs a note-perfect performance that i could get by listening to the recording.