If I'm not mistaken, I believe the bins used at LAX are serviced by a contract. I think these are the bins with the advertisements printed inside of them. My understanding is that TSA is prohibited from cleaning or replacing these bins. The contractor is supposed to do that.
As for the cleanliness of the bins, I think it's an unrealistic expectation. At SAT, we take away bins that are cracked, soiled or stained. On slow nights, we wipe them down with alcohol (it's the closest thing to cleaning supplies we have), but that's about the best we can do.
As for the dirty floors, I grant that the floors are not clean (even though our airport maintenance cleans the floors twice daily). However, if there is one thing universally associated with airport security, it's the idea of having to remove one's shoes as part of the process. Even those who travel infrequently know that they have to remove their shoes. Why not pack an extra pair of socks for the specific purpose of temporarily wearing them while processing through security? (What I find ironic is that many people wear their shoes barefooted, and whatever germs one may pick up on the floor probably pale in comparison to what resides inside the shoes themselves!)