Fixing the neutral bar problem is easy: Simply loosen the screw, remove one conductor, and relocate it to a different screw. But make sure the breaker for that circuit is turned off before you do anything! Make sure all the screws are tightened down tight.
I would assume the subpanel is fed from a single pole breaker. That will need to replaced with a double pole breaker, but there's no more room in the main panel for one. Probably the easiest thing to do would be to see if there are any circuits that are lightly loaded and possibly combine them.
For example: Let's say there's a 15 A breaker that feeds a bedroom, and another 15 A breaker that feeds another bedroom. Instead of having separate 15A circuits for each bedroom, you could combine them and put both bedrooms on one circuit. The electrical stuff you typically use in a bedroom usually doesn't use much electricity, so you probably wouldn't have a problem putting 2 on one circuit. By doing that, you can eliminate one of the 15A breakers and free up a space in the panel.
Keep in mind that whichever circuits you want to combine must be the same amperage (don't combine a 15A circuit with a 20A circuit), and there may be code restrictions on which circuits you can combine. For example, some receptacles are required by code to be on their own dedicated circuit, so you wouldn't be able to combine that circuit with another circuit. So basically, IF you decide to go this route, check here with us first and tell us which circuits you're thinking of combining, and we'll tell you if it's allowable or not.
Another option is to mount another subpanel right next to the main panel and relocate some circuits to it, thus freeing up some spaces in the main panel.
