Ok, a few things. Obviously this is a DUI case, and obviously the defendant is represented by the Public Defender's Office. You bring up a few interesting points here in your angry rant. I'll try to take them one at a time.
Can the DA drag a case out forever? - No. The defendant had to waive time, and his/her attorney had to continually agree to the continuances. A defendant accused of a misdemeanor can demand a trial within 30 days at any time. This may be unwise if they are still gathering evidence.
What do you do if the police lie in their reports? - Join the crowd. The defendant's attorney can try to trip the officer up in cross-examination if they tell inconsistent lies. This is why we have trials, and why a good lawyer makes for allot of angry cops.
What can I do if the Sobriety is done off camera? - Nothing. The police don't have to record their arrests. Most police agencies in California don't even have videotaping equipment in their squad cars.
What can I do about the prosecutor orignally saying there was no video, and then comming up with a video later on? - Nothing, but I'm not sure what you are angry about. Did you want the trial to go on without the video? The attorney could have demanded a speedy trial and gotten this done. Did you want to review the video prior to trial. Great, now you can. You could theoretically ask for sanctions agains the prosecution for producing late evidence, but this will almsot ceratinly be denied unless a pattern of misconduct can be seen. Also it seems odd to me to hear that the "defendant" "filed for discovery" "at the first hearing." There is no "filing" for discovery. A request needs to be sent to the District Attoreny's Office. If this wasn't done, asking for things in open court wouldn't get the defendant anywhere. The request certianly is never "filed" with the court. If such a request was properly made, and ignored, 15 days later a request to the court should have been made to compel the prosecutor to produce the requested evidence.
Now. As to the actual highlighted question - Can a defendant be barred from viewing the dashcam video? - Normally no. I can't imagine why a judge would do that. I'm not sure I believe that they did. If the video was going to be used as evidence at the trial it would need to be played in open court. The judge would gain nothing by making this kind of order. If the public defender simply doesn't want to take the time to play it for the defendant, that is another matter. Usually these kinds of things get sorted out by asking the judge to assign a new public defender. The request is called a "Marsden Request."
By the way did you say a "urine test" was done? Who is still using those? Was there really no blood or breath test given?
Whole case sounds fishy.
Mr. Hagopian answered your question quite thoroughly. You have an attorney, so you really need to be discussing these points with him or her. If it is a public defender, then you should consider hiring a private attorney. You have a lot of viable issues, which a good attorney could address. Good luck!
The above stated is advice only, and does not establish an attorney-client relationship.