After reviewing some of my telephoto shots, it does look like the ones that are the softest are ones where the shutter speed is definitely too slow. One of the reasons for that was that I was shooting in the failing light outside. I guess in that circumstance I would definitely need to be using a tripod. Ash, you mentioned turning SR off and using the 2 second timer when mounted on a tripod. Sorry for my ignorance, but why turn off SR when using a tripod?
I will also make sure to in the future not recompose my shots after locking my focus and see if I see an improvement.
I've attached two pictures. No PP done at all except for 100% crop of both images. I know that they are not perfect exposure-wise (and I realized I accidentally cut off the goose's head in the reflection), but I just wanted to provide a couple of examples.
The goose: 230mm, F/5.6, 1/320, ISO-400, manual
Maybe not too bad, but I may have missed a little since he/she was moving in the water.
The rabbit: 300mm, F5.8, 1/20
, ISO-800, Av priority
I think I now know why I was so off in this one.
I'll try again with my new found knowledge and hopefully post later with some better results. I've got a crazy work week, so it may be a few days before I can get out to take more pictures. Thanks again everyone for the help, and if you have any more suggestions, I'm definitely open to them.