First, I want to say that I'm not trying to beat up on you. Everyone was new at this once. However, you do have some serious problems with your system, if you want it to house anemones.
Looking at the second picture, you tank does not have nearly enough live rock. Typically you want about 1 pound of rock per gallon of water as a minimum. I can see just by looking at it that your not even close. In a typical SW reef system LR is the biological filtration system. Failure to have enough is going to result in low quality water.
Looking at the first picture. It's tough to really tell, but it looks like your lighting is not enough for an anemone. The tank just doesn't seem bright enough. Typical lighting I'd like to see for an anemone in a tank this size would be four T5 florescent bulbs, or two serious LED fixtures such as two AI Hydra 26's. These are typical examples, similar lighting from other manufacturers would be fine. Keep in mind that " nuclear zoas and a grooved brain" are low light corals, and require far less light. If you do increase the lighting, up it slowly, don't do it all at once.
I don't see any kind of skimmer on the system. Yes, it is possible to maintain a system without one, but I consider a skimmer so "highly desirable" that I would not want to run a system this size or larger with out one.
Your system is also far too new for an anemone. You usually want to have the tank running for about a year and stable before you even attempt one. Let me guess a little on this one the guy at your LFS said you'd be fine adding the anemones. Am I right?
The good news is that once you correct those issues, and wait until the tank is stable, there is no reason you can't keep an anemone.