what's wrong with my bass?

[Webtroll]

I'm thinking the battery faded around the time he changed the strings. After changing the strings he probably played it more and left it plugged in once or twice speeding up the drain. The other damage isn't related but if the nut cracked maybe he oughta get it looked at. If it didn't crack the scratches are nothing but an observation when trying to figure out why the bass was sounding strange.

Seriously, put a new battery in it and see if you still have the same problem. It could be an easy fix, you may have a bigger problem. The symptom is a common drained battery symptom.

 

[Bassorama57]

The only problem with this is that if everything is in equal temperment and you are closer to pure intonation you will sound out of tune. There is no way to make a fretted instrument sound in tune.

No worries, just answering the question. Frankly I'm not an engineer, but I can't tell any difference between it and my Fenders, nor can I explain from looking at it how it'd work.
Only point being that if the nut is craked, it needs EBMM factory parts support (and they don't sell replacement parts direct to the public). or you can just put a Bust-A-Nut or some other aftermarket part in there - but it's a limited edition, so I'd think the OP would want to keep it stock.

I change my batteries (a) every six months (b) before any major shows (c) if I consciously note that I've left it plugged in a lot or used it a lot or (d) if I happen to have unused batteries in my gig bag that I can't remember buying whichever comes first.

 

[Webtroll]

I change my batteries (a) every six months (b) before any major shows (c) if I consciously note that I've left it plugged in a lot or used it a lot or (d) if I happen to have unused batteries in my gig bag that I can't remember buying whichever comes first.

spoken like a man who has owned active basses for a long time