Should the military allow servicemembers to be in tv shows or movies?

Movies are always better when somebody from the military helps. I hate watching movies that cost $100M to make but are ruined because they couldn't get a single competent military person to point out tons of silly mistakes.

Let's avoid having this...
https://www.rallypoint.com/answers/most-memorable-military-movie-discrepancies

NWLA is surprisingly a huge movie production area. Barksdale has been showcased in the movies The Guardian and Battlefield earth. Both of which have extras from the base. I personally am an extra in Texas Chainsaw Massacre 3D. I have a troop that was in Vampires Suck. Know folks that were extras in Harold and Kumar escape Gitmo, Year 1, the TV series Salem, Drive Angry, Snitch, and that is off the top of my head.

Everyone I know did it on thier off days, on leave or on Comp Time Off (CTO).

I don't see why not, currently policies are in place:

http://www.army.mil/info/institution/publicAffairs/ocpa-west/faq.html

http://www.hqmc.marines.mil/divpa/Units/LosAngelesPublicAffairs/FAQ.aspx

Navy and Air Force have similar policies under the auspices of the their public affairs

As long as they are not getting paid for it i don't see an issue with it. I think it helps bring a sense of realism to it because if the service member is doing a tactical part then it will as close to real as possible instead of watching a moving and going wow that was Hollywood right there.

DoD is heavily invested in film production and has dedicated offices just for working with the industry. Oftentimes a producer will want military assets or personnel. Many times they don't want to fo that route because the service branches want to review and correct the script in return so as to ensure accuracy or correct a negative portrayal. The Navy was heavily involved, of course, with Top Gun, as they are with it's sequel. They often also use vets to portray servicemembers. Those vets, however, are often not the A level actors who bring in the money.

This is a question that can answer from actual experience. While serving in West Berlin in the mid 1970s, a number of extras were needed in the making of a movie. Most of those extras were to be American Army members in Class A uniforms. I, along with several others from our unit, was chosen. However, it was to be on our own time and we could not wear our own uniforms. Wardrobe from the movie company provided appropriate uniforms for us to wear. We were paid 50$ a day for two days work and received lunches as well. As we were joint service with the Air Force, it was humorous to see people we knew were Zoomies walking around in Army greens. By the way, the movie was "Inside Out" (aka: Hitler's Gold), with Telly Savalas and Robert Culp.

Yes, (on leave) unless they have high clearances. It is a security concern to globally identify spooks and spies.