Putting on a straight stitch foot will make it real easy to tell if the feed dogs are aligned or not.
I would not think it matters - UNLESS someone put on a Satin Foot and not a regular zig zag foot. but if you want to rule out the simple stuff first, that is where I'd start.
I just went and looked at my 28 - (same vintage) and I would bet that using a zigzag foot on this machine WOULD cause problems. It is differnet than my 27, 66, 15 and 201 (didn't look at any others). There is almost NO feed to the left of the needle. It is to the right and behind.