The tripod head's tilt will not lock in place - can anyone that knows tripods tell me if I'm missing a piece like a rubber washer?
Even when tightened down all the way the tripod still tilts to the front and back when weight is applied.
I don't know about that model specifically, but that's a pretty typical design for a pan/tilt tripod head. Turning the handle clockwise squeezes the right side of the head around a shaft, increasing friction and eventually locking the tilt mechanism. I doubt that you're missing any part; it's far more likely that some part is worn out. It looks like there's some red plastic or rubber material caught in the area that should compress as the handle is turned.
To attempt a repair, I'd start by gently prying the red "Albinar" medallion out -- it'll probably just pop out. You should then be able to see whether there's some plastic or rubber material that needs to be replaced or whether the metal collar makes direct contact with the shaft or bolt that it compresses. In the latter case, the problem may be that the metal parts are simply worn and you'll need to add some shim material to help increase compression. It looks like the parts are otherwise in decent condition -- the threads on the handle look good, the collar isn't cracked, so there's no reason that you shouldn't be able to restore this head if you want to. A great source for metal shim stock and different types and thicknesses of rubber and plastic is mcmaster.com.
On the other hand, you can buy a brand new pan/tilt head of similar or better quality for around $25. Unless you're really attached to this one in particular, it may not make sense to repair it.
If you didn't get any solution for your tripod head you can try another one.
Have you tried to unscrew the head and check if is 1/4" screw?
If is 1/4" I recommend this tripod ball head, I bought this a month ago and I'm very happy! It's very solid, good built. Check this out: http://www.ebay.com/itm/200906660145