Recognizing a Welsh accent
If you're into phonetics, Omniglot's Welsh language, alphabet and pronunciation guide seems like a good place to start. IDEA's Dialects and Accents of Wales has some thorough recordings. The text transcriptions are particularly useful as they mention features of that specific accent sample.
From a more pop-culture perspective (read: American), Catherine Zeta-Jones is Welsh and sometimes uses her Welsh accent in interviews and such. It is sometimes possible to detect the Welsh coming through when she speaks with an intentional American accent in movies.
From my experiences speaking with my UK friends about accent stereotypes, a Welsh accent could be considered the cultural equivalent of what a "country" accent is here in America. But we'd probably need a real, live Brit to corroborate or elaborate further.
As an aside, detecting the difference between an Irish and Scottish accent qualifies as pretty good? Come back when you're picking out Liverpool from Leeds. Okay I kid, but only slightly. :)
If you want a lot of Welsh accent to listen to, find a recording of 'Under Milk Wood' by Dylan Thomas, preferably read by Richard Burton. You don't get more Welsh than that, and it may help you close down on a welsh accent.
It should also be noted that if you want to pick out a Welsh English speaker, there are a few lexical items to listen out for, borrowed from the Welsh language (e.g. mam, cwtch, dwt etc.) But there are a few phonological aspects too, such as a rolled Rs (and even rhoticity - pronouncing the is car - in certain Welsh varieties of English)
If you want to go even deeper into this, a Cardiff accent is pretty notable amongst Welsh English varieties due to the notable pronunciation of the vowel in the words Cardiff, Arms Park and smart where, to give you an orthographic representation, they would sound more like "Cerdiff", "Erms Perk" and "smert" but this is a very stereotypical, broad pronunciation.
But I'd have to agree with the above posts that the best thing to do would be to go on youtube and listen to some Welshmen and women. The comedian Rhod Gilbert, from Carmarthen, has a fairly broad Welsh accent but people do normally think of Tom Jones when thinking of a Welsh English speaker - but it's not unusual.