I was in a bike shop today to try to get my bike fixed because the chain skips and its been getting worse. One bike mechanic looked at it and seemed to say it wasn't worth fixing. He said something about getting a new chain, front and rear sprockets and bearings. After spending some time on the internet looking at this problem, I found out about a problem known as chain stretch where the pins and bushings wear out and the chain ends up longer compared to when it was new. I checked for that and other things like derailleur alignment, etc. I tried turning a screw on the derailleur to see if the chain would tighten up, but it didn't help. The derailleur tension is about the same compared to some other bikes I have, so I don't think its that. I made two videos which seems to show the bike has a lot of chain stretch and doesn't line up on the sprockets. I'm going to try to change the chain myself and see how well that works. I checked the chains on three other bikes. Two don't seem to have the problem at all and my 1973 Schwinn Varsity might be developing this problem a little bit, but it hasn't had any problems with a skipping chain and sprockets. The Bianchi Nyala is the worst one.
bike chain appears stretched
https://www.youtube.com/watch?v=5LUokZuXWZ8
chain and sprockets don't line up
https://www.youtube.com/watch?v=iDd_Meg-eso