The problem turned out to be as follows:
1 - somehow the TT created and additional "phantom" W-2 for my spouse with some missing information on it (the original proper W-2 was still there, so where is that extra copy of W-2 came from is a complete mystery to everyone)
2 - when entering information for local taxes for Battle Creek, MI, I've entered the "Locality Name" as "MIBATTLE" -> exactly as it is shown on the W-2. But the TT wants it to be entered as "MI-BCK"
Once the 2 issues above were corrected, everything started to work right.
