I am a child safety seat technician and figured I'd add my 2 cents.
Slyangel9 is right with putting weight in the seat and tightening up the belts, whether it be the seatbelt or the latch system belts. I would not recommend putting a seat in with the latch anchor points if its not a latch position, in the center the seatbelt will work just fine.
As far as a seatbelt not working in the center position but working on the outboard positions, I have never seen this, it should work in any position. The seat is another story, if there's a hump in the center or an armrest that prevents it from going there, yes by all means use the outboard positions.
The only thing I can think of with a seatbelt appearing to not work would be if you have an older model Peg Pereggo infant seat. This seats base was a horror to install. It could be done but was not user friendly to most parents. This has since been redesigned, which falls back to the previous statement, A $60.00 investment in a new seat is a small price to pay for you child. I practice what I preach, 3 children and never used the seat for more than 1 child. Improvements to newer seats each time outweighed the savings.
Another little trick for people with leather seats is to buy some drawer line, the stuff you put in kitchen drawers under utensil's. Match your color, cut to size, and it saves the seat and helps with the slippery nature of leather seats.
One other thing to keep in mind, once you get a good seat installation. The install is only as good as how well you secure the child in the seat. Try to avoid bulky jackets under the belts. Only 1 finger should fit between your child and the belt, just below their shoulders, when tightened correctly.
Out on Long Island in N.Y. its the police agencies that do most installations. Give your local police a call and hopefully they'll install it or guide you to a location to hhave it done.
These 2 web sites also offer some good information when you follow the child seat links:
http://www.nhtsa.dot.gov/portal/site/nhtsa/menuitem.c1a4b135ea7fc398d33a431046108a0c/
http://safeny.org/sesa-un.htm
Hope this helps,
Pete