I always try to look at the deck's art style as a whole, so it's rare that a single card will ruin everything.
That being said, I've noticed that the Tower is a card that I look out for in particular. Most decks stick to the traditional "building hit by lightning" image, but I really do want to see some creativity in how that is presented. I tend to prefer beautiful and fanciful illustrations, and if the Tower doesn't resonate with me, I get disappointed and become more critical of the deck (meaning the other cards *really* have to make up for it).
Also, a major card for me is the Queen of Swords. I really identify with her traditional meanings, as well as personal meanings I've ascribed to her. I absolutely think of the QoS as me in the deck, so if she looks ridiculous or otherwise less than awesome, I'll probably pass on it. (Yeah, I'm selfish and petty XP) Conversely, a great QoS can make up for other art in the deck that doesn't speak to me as strongly.
Finally, I check to make sure I can live with the portrayal of the Lovers. This is another card that, like the Tower, kind of needs to be done right. Even more so than the Tower, I'm critical of the Lovers because it needs to speak to the duality -- the spiritual attraction or recognition -- that the card points to, even more so than "love." Two people embracing on the Lovers? *Que eye roll*
Okay... right.
In general (there are exceptions, of course), I'm not a fan of the overuse of CGI in the artwork, actual photos or photo-realistic portraits (I can't get past the fact that these are other humans with their own lives and stories... and they're popping up in my cards?!), collages, and contrived alternative names for the Major Arcana or Suits. Also, images of people who look unnaturally posed or are in contrived poses. These things just don't fit into my personal artistic aesthetic.
I could go into great detail about why I take issue with certain aesthetic elements, but it would definitely be harsh... and I do at least recognize that 1) the artists put a lot of time into these decks, and 2) a great many other people like the decks I don't - and that's totally great! Everyone is entitled to his or her own opinion.
I never thought of myself as very picky, but when it comes down to it, I will be or already have been spending a lot of time (and sometimes money) on these cards. I don't want to be put off by them; I don't want to regret having bought them; I don't want them to make me feel uncomfortable. To the extent that I can be, I want to like and find meaning in every image of the deck. If I can't even bear to look at an image without thinking "wtf," I'm not going to find that meaning, which renders the deck more or less pointless.