Depositing a check with both wife's and my name into my sole account

Absolute worst case is that the bank notices this and puts a fraud alert on your account and locks it until you get it sorted. Although, the chance of this is essentially zero since no reasonable person would assume ill intent in this case (but you never know).

Regardless of if they lock it or not, most likely they will ask that your wife provide some identification and verify that she approves of the deposit. Since the bank has already taken the check and credited you the money I would say the chances that they come back and invalidate it is very low. Just leave it be for a couple weeks to make sure it sticks. If you want a quick resolution you can call the bank. You bringing it up to them would essentially prove that you had no ill intent.

While I don't have a canonical answer to this question, I can share a couple of similar experiences. I've had this happen a few times whenever we vacate an apartment after the completion of our lease, the landlord would typically refund the security deposit back to us with a certified check made out to both me and my wife. Since I put down the deposit, I would just cash the check into my own account with mobile deposit and never had any issues with it.

This last time since we've moved out of the US, the check was mailed to my sister and instead of her forwarding that via international mail, I asked her to deposit the check in her account, which she did with mobile deposit. The check cleared promptly and she e-transferred the funds to us.

Based on my observations and some reading into the check clearing process, this is mostly automated with very little human intervention. Banks don't verify signatures or anything else either. The problems only arise when accounts don't have adequate balance or the checks are fraudulent. Upon a transaction being reversed humans get involved. So I think in your case you should be absolutely fine, even in the case that the bank flagged the transaction, you wouldn't be out of the money. It would just be a little more hassle.

I've had a similar situation with a $12 check deposited electronically into my Ally checking account. Whatever automated process there is running on their side flagged the check as being written out to 2 individuals but only having one signature so they rejected the deposit sometime within 7 days.

I just had to get my wife to sign it and then resubmitted it.

Not sure how they handle it with a physical check but assuming they don't mark it as rejected or invalid you should be able to just get it fully signed and deposited.