A agree with Andy here. When DET-5 was first started the team patch included some military-specific insignia. We changed that for the same reasons that have been mentioned here. I don't wear a service-branch tape on my BDUs, instead I use my team, whether it's DET-5 or SWAIRTAC. I believe there are some regulations about wearing a U.S. flag patch on one's uniform, but they are rarely enforced (just like many of the other regs pertaining to the presentation of the flag...pet peeve). I believe there are also laws regarding the wearing of "U.S. Army" insignia and ID tapes on clothing. Rule of thumb: If you haven't earned the tab or patch IRL, don't wear it.
The situation for Law-Enforcement (LE) patches and insignia is, if anything, even more serious then for military ones. I would strongly reccomend against wearing department or unit patches when playing airsoft, and if I encounter someone wearing them, I will - unofficially and politely - ask that the person remove them. By appearing to be a law-enforcement officer one is committing a crime, even if one does not specifically state "I am a police officer". At the very least this will engender a severely negative attitude in any law-enforcement personnel encountered while wearing the insignia. The worst-case scenario is arrest, confiscation of one's airsoft guns and uniform, and, eventually, legislation aimed at restricting or banning airsoft. Needless to say, this kind of negative interaction with the authorities is something we, as airsofters, want to avoid.