I’m certain that there is some degree of control in the Radio industry that keeps folks from annoying the advertisers (e.g. don’t bite the hand that feeds you), but I would like to know if the typical boilerplate contract for an advertising spot makes clear statements about not discussing the ad content.
Once in a very rare while I hear a DJ make some joke about an ad – a couple of years ago one station ran ads for XM Radio (satellite radio), and the two DJ’s couldn’t control themselves: they kept shouting “It’s the competition, you morons!” in the background throughout the ad.
If this happens, does the station simply re-run the ad? Do they refund it? (e.g. you bought 40 spots and we messed up one, so we’ll bill you for 39)
How about live reads that are bungled or laughed through? Who determines if it was done properly?
Do the advertisers have any legal say in the content immediately before or after their spots?
I’m a former DJ, so I can speak with some authority, but only in regards to the market I was in.
There’s always the potential of angering your advertisers, but honestly, it happens very rarely unless you’re simply trying to piss someone off. During the commercials is when personalities are usually “prepping” for their next on-air bit, so I very rarely paid attention to anything that was running, other than to watch the digital display to make sure I fired the next commercial when the first one was ending.
We’d goof on national radio spots occasionally, particularly annoying or inane ones, because those were least-frequently monitored. Realistically, Pepsi is probably not going to get bent out of shape about a muffed commercial than, say, a local advertiser. Local advertisers are counting on a significant Return On Investment, so if you blow their spot, they’re going to be angrier than Pepsi, who is only looking for commercial “coverage” to keep their product name in your brain.
If we were doing a “live read” and it got muffed for some reason, we’d usually throw in another mention later on. IIRC, no advertisers ever demanded a refund on one muffed spot, because they’d need to be paying people to listen to the radio for each individual read.
Mostly, however, we didn’t fark around with the local advertisers because it’s in the DJ’s best interests to cultivate good relationships with local businesses. Building a good sense of community helps create loyalty and a loyal fanbase, which in turn can keep a DJ in a job.
Plus, if you piss off the local pizzeria who advertises, there’s much less chance of said pizzeria bringing you a free pie during your late-night Saturday shift. 
Ad man, here (wow, all of the relevant players are checking in, aren’t they ?)
The bite-the-hand-that-feeds-you thing is what largely prevents problems. This is a TV example, but Rick Reilly tells of the time he was in the booth and followed a LaQuinta spot with the old line, “LaQuinta is Spanish for ‘next to Denny’s.’” He says the director yelled into his earpiece that “we never make fun of the sponsors.”
As Chastain86 says, this is less of a concern to national advertisers than local ones, but if, say, Howard Stern or Bob & Tom were to follow a Pepsi spot with a protracted discussion of how terrible their product was, it’s a good bet the show would need a new sponsor soon.
The make-goods on muffed spots can vary widely, and are negotiated on a case-by-case basis. Usually a re-read is fine. If a recorded spot couldn’t be heard, usually it will simply be run again later.
No advertiser has any say regarding the content preceding or following their paid time. This would give sponsors the ability to censor the airwaves. Fortunately, the broadcasters need the sponsors and vice versa, so everyone generally plays nice.
One of the album rock stations in my hometown had a morning team made up of the typical funny gut and straight man. The “funny guy” reminded me very much of David Letterman in that he always sounded tongue-in-cheek and it was hard to take anything he said seriously. I always thought that the ads he recorded sounded like they had some kind of sarcastic subtext, just because it was his voice reading them, even though that was obviously not the intent. And sometimes I wondered whether it bugged any advertisers as well.
If an advertiser chooses to have a station personality record the voice-over (as opposed to hiring outside voice talent to do it), then the advertiser can often choose which personality he’d like.
I suspect your Letterman clone didn’t irk the people who selected him. (Unless, of course, someone else was recording their spots the next year. 
)
Sometimes, though, the advertisers are happy with the mention and have no problem with the DJ insulting their product. Don Imus used to read an ad for a particular Men’s Shop and say that the sleeves would fall off any jacket you bought there. Evidently, the store involved had no problem with this, since Imus did it for months.
<Semi-relaed anecdote> In the aftermath of the Columbine shootings in Colorado, Howard Stern made a very crude comment (!) about the situation on air. A Denver jeweler, Tom Shane, who has outlets across the country (Shane Co.) and is a relentless radio advertiser, pulled all his spots not only from Stern’s show, but from any station than runs Stern at all, and to my knowledge still hasn’t changed his policy. <SRA>