some times the end of the bulb is worn and not quite long enough to make good contact. The spring in the socket is weak/compressed.Try brand new bulbs and that should help. also the socket housing may need cleaning where the nubs hold. Not sure what soldering you are referring to but most sockets have insulated connectors on the end and not really anything to solder without possibly creating a short.

It is simply moving the connection to the center contact instead of using the tab to eliminate a possible bad contact between the two parts. the added solder blob is just making a connection between the outer housing and bracket instead of relying on a crimped together connection. If I were going to do all this soldering I would resolder new sockets in. Try NEW bulbs first.