If I am wrong about this please let me know. There is nowhere within adwords to view the actual (approved or pending) status of a new ad. They leave you hanging, wondering if the ad is actually available, or is not running for some other reason. I did a search on this problem and found that it existed, AND people were complaining about it, in December of 2005. My favorite quote- "Are they stupid, or just lazy?" Alan
You can use the diagnostic tool to see if an ad is showing. But no, there's no where to see an ads approval status, unless it's rejected. Related: http://adwords.google.com/support/bin/answer.py?answer=14072&topic=29
Sometimes... You can shoot them... But you are right, it's insane. And it's not that hard to implement a "your ad has been approved" light somewhere.
As near as I can tell the diagnostic tool that GuyFromChicago mentions, is only available for keyword ads. I do not use keyword ads, because my customer base is very narrow (Spanish speaking people who know some English and want to improve their English pronunciation). I got to realizing that in the time that this problem has existed it has cost them more money (man-hours responding to customer complaints) than it would have to hire an extra person to fix the problem. Alan