I could tell the SEs that cart.php is off limits by using robots.txt, but - do they care? Will I rank better for it? Is it worth my time and the risk that I might make a mistake ("don't fix it if it ain't broken")? I must be getting old, a few years ago I would just fix it... 
Definitely fix it - it is broken!
You really don't want those URLs to be indexed. If they are indexed, then each searcher visiting your site will, on entering your site, add the item in question to their shopping cart! You might think that's great, but they won't - and they are likely to leave, confused or angry.
Also, by excluding pages you
don't want to be indexed, you give the spider more opportunity to see pages you
do want to be indexed. A spider will only spend so much time on your site, particularly if it sees a lot of essentially duplicated content.