Col,
The special weapons are technically not that special - except that most police officers do not carry around fully automatic assault rifles when on patrol. Even SWAT officers don't carry those except when on a special call-out, like a barricade in the barrio, captives in Capistrano, ensconced embezzlers in Encino, or such as that.
They get to shoot tear gas (technically, a lachrimation agent that has more than just a few tears associated with it) and use "flash-bangs" (explosive devices that make a bright light and a lot of noise as a distraction). They get to kick in doors or blow the locks with a small explosive charge.
As to the popular TV show S.W.A.T.? First and foremost, that is a rehash of a series from YEARS ago, like 1980s if I recall correctly. They even used the same theme song! The star of the older version was, I think, Steve Forrest. Now they have the brooding Shemar Moore - and the team members are a bit more diverse this time.
The S.W.A.T. program only shows dramatized situations because, ... well... it IS a TV drama, you know. Ratings on TV get boosted by many things, but when you don't have exceptionally literate scripting, the next best thing is a little violence sprinkled copiously with car chases. I would ask you to consider that the S.W.A.T. program is more in the "bread and circuses" style of TV rather than any truly informative style.
My cable provider in New Orleans offers multiple channels including one called "Crime and Investigation" - the C&I channel - where some shows follow real S.W.A.T. groups who go out on various missions. More often than not, they are simply serving a warrant at a home expected to be full of people who would actively resist.
I can't be sure, but I THINK the goal for the real S.W.A.T. officers is not to use their weapons, but to have them showing in a way that the people at the home realize that resistance would lead to their immediate and probably painful deaths. What is that principle from the Art of War? The best way to win a battle is to persuade your enemy to not start one?
As a result, in those C&I shows, the most common violence is bashing in a door or using an armored vehicle to pull down burglar bars. Rarely do the C&I case studies show actual use of firearms. Brandishing? Yes, accompanied by lots of yelling and screaming. Firing the weapons? VERY rarely.