If you're looking for specific characteristics of particular accents, there are a couple I have noticed that have been fairly reliable.
I'm usually able to tell whether someone is from Shanghai (or a nearby Wu-dialect area) based on the way they pronounce the word 能 (néng). Instead of the standard [nəŋ], they often say [nəɲ]. Note the [ɲ] (a palatal nasal sound) rather than [ŋ] (a velar nasal sound). You can hear the differences on the Wikipedia pages that I linked. If you happen to listen to ChinesePod, you may notice that Jenny typically pronounces 能 this way. The reason for this particular pronunciation is because in Shanghainese and other Wu dialects, [ŋ] and [ɲ] are allophones of the same consonant and [ɲ] always occurs after the vowel /ə/.
Tianjin folks sometimes pronounce initial w- as [ʋ] (a labiodental approximate sound that sounds somewhat like [v]). There was some discussion of this sound on a post in the Beijing Sounds blog. I don't necessarily know the real explanation for this, but this sound did exist in Late Middle Chinese (ca. 1200 AD) and is transcribed by linguists as mv- (see note 2 under the table in this link). All the mv- sounds merged with w- and Mandarin and m- in Cantonese (e.g., 未 is wèi in Mandarin and mei in Cantonese), but it might be that in the Tianjin dialect w- merged with mv- and both came to be pronounced as [ʋ] (this is purely my speculation though).
If we go to more general dialectical characteristics, you can often find free variation of initial n- and l- consonants in the south, particularly in Cantonese-speaking regions. There is also free variation of h- and f- around south-central China (i.e., Hunan region). The latter probably has something to do with the fact that many /x/ and /ɣ/ sounds in Middle Chinese shifted to /x/ or /f/ (which correspond to pinyin h- and f-, respectively) in various modern dialects.