The more the public knows about the criminal justice system, the better.

Subject to appropriate safeguards, there's no reason why theremany cases shouldn't be televising of very many casesed.

The original was indirect and rather awkward.

MCurrently, members of the public, are denied seeing a real criminal court in action unless they're there in person.

The 'currently' helps connect this sentence with the previous one. The word 'are' was added to make this a complete sentence.

However, many vidoes just show clips about trials and they have few accurate portrayals . Sometimes, they cand even present a misleading picture.

Something about the 'and' typing together the 'few accurate portrayals' and the 'even present a misleading picture' just didn't feel right. I can't put my finger on what it was, though, so I've marked for style.

Subject to appropriate safeguards, there's no reason why theremore cases shouldn't be televising of very many casesed.

The meaning is a little different in my correction (saying that more cases should be televised vs very many cases should be televised). However, I can't think of a way to say "very many" cases should be televised without it sounding clunky and childish. "More" is the typical usage here.

Generally, "there shouldn't be" + an infinitive verb (like televising, running, etc) should be avoided if possible, it sounds awkward. This phrasing works better with noun phrases (e.x. "there shouldn't be a problem")

Members of the public, denied can't seeing a real criminal court in action unless they're there in person.

In this age of mass media, most people derive their knowledge of what goes on in a court from what they see on videosTV or in videos online.

"what goes on in a court" can be replaced by the more concise and formal "court proceedings"

However, many vidoeos just show clips aboutof trials and they have few. Few are accurate portrayals and some even present a misleading picture.

This is sort of two ideas, so splitting into to sentences is appropriate and adds some nice variety to your piece. It's generally a good idea to use a mix of long and short sentences in your writing.

The oOfficial releases of complete trial video ensuringe that the public can gain first-hand experience ofwith how that system works.