Big thanks for all your suggestions. They make sense to me. Funkshwey... I think you may have nailed at least a few "issues". I definitely do dig in too much. When talking with Sheldon yesterday this came up. I want to re-train myself to play with a much lighter touch. In fact this was one of the main reasons I decided to go with a DW. Toward this end, Sheldon suggested adjusting the truss rod - to lower the action and have the fret buzz that will result from digging in too much be an immediate "negative reinforcer". He also suggested I turn my amp volume up louder than I normally would as an additional encouragement to play with a lighter touch. I like this idea too (what bass player wouldn't). Your other comment about exactly where I'm positioning my left fingers when fretting e.g. not right up against the fret, was something I wondered about affecting pitch. Again, I'm realizing I do need to do some retraining of my fingers to the fanned fretting.
Spiritbass... you're confirming for me what I wondered about, i.e. maybe my DW needs a more precise tuner. Yesterday, I went to my local independently owned and operated music store and asked if they had any Peterson Strobostomp tuners (he didn't). The guy asked if I wanted to tune a cello or violin. I told him about my new DW (which he'd never heard of and tried to sell my a Lightwave bass) and he told me a strobe tuner for a bass is overkill! I don't agree and I'm glad to hear some of you do think our DW's benefit from extremely accurate tuning.
Finally, BuffaloBob... I don't know if my cd player is out of tune. It's a Sony ES 555 (their "audiophile" line) player. However, I do find that almost every cd I play is not precisely in any particular key. More often than not, songs are between keys. I'm lazy and prefer not to retune my bass with each cd I play... but maybe I need to start doing this. Maybe I'll get the Tascam with adjustable pitch...
Again, thanks mucho for all your intelligent suggestions and comments. I'll get back to you.
Burt