3. Space combat. This one is kinda a case of rule of cool. Realistic space combat wouldn't look like much. But really, the ranges involved in BSG are much too short, both for weapons fire and for targeting/detection.
4. Living ships. Seriously, this one's been done by every major soft science fiction series in the last 15 years, and has got to stop. Living tissue has no place in spacecraft design, except the warm meatbags who fly the damn things (and possibly as part of their life support).
I have to give BSG a lot of credit for space combat because they did allow ships to turn 180 while still traveling in the same direction. Most space combat I've seen treats the ships like aircraft instead of rockets, so I was very pleasantly surprised. Also the ranges used are done so for dramatic reasons vice realism. Top Gun for example has aircraft almost touching each other in combat scenes, but if they showed actual ranges then all you would be able to make out on your TV would be a speck. I don't fault the movies for this because they want to emphasize what the pilot sees, not what it actually looks like.
As for living ships, I know it's been overdone, but I like the idea. We are always finding creatures in unexpected places on our planet and there is no biological limit to living in space other than the need for food and oxygen or whatever the organism lives off of. Sure it's beyond our level of technology, but it's not impossible and it could potentially have benefits such as repairing its own injuries. Why are you so set against the idea?
Stellar rays prove fibbing never pays. Embezzlement is another matter.