Native Polish born in Upper Silesia here. Here is my answer: When a native Silesian of older generation (say, 60+) speaks standard Polish, he/she has a strong regional accent which includes following features:
Nasal vowel ę before consonants, is completely decomposed and shifted towards 'yn'. Std. Polish 'ręka' is typically pronounced renka with a slightly nasal 'e' and a weakly pronounced 'n'. The Silesian pronounciation is 'rynka'.
Nasal vowel ą is decomposed to 'ón' or 'óm' Dąb: standard Polish 'Domp' with slightly nasal o and a weak m, Silesian Polish: Dómp.
Combinations 'en', 'em', 'on', 'om' are pronouced as 'yn', 'ym', 'ón', 'óm', for instance "Cyntrum", 'Kónkuryncja' etc.
Difference between u and ó is maintained while speaking standard Polish.
There is a difference in pitch (intonation), especially in questions, which have a falling intonation (in Polish, the intonation rises). I can provide you with audio examples per Skype:)
For younger generation, the regional features are not so strong, some people are completely 'bilingual' and swich to std Polish with absolutel no accent. However, people who speak Silesian at home usually are not able to eliminate the above listed features while speaking Polish.
The answer given above 'jo myśla' instead of 'ja myślę' is not true: it refers to the dialect, and the question was about the regional pronounciation of standard Polish. Today, almost all speakers of Silesian are able to switch to standard Polish, and they would say 'ja myślę'. However, the differences listed as 1-5 will be maintained.
There is also some vocabulary and very little grammar stuff which Silesian maintain even while speakig standard Polish:
1. Kołaczyk (pl: drożdżówka)
2. Tyta (pl: does not exist: a paper conic tube with sweets which is given to children on their first school day).
3. Zalecki (pl. Wypominki)
4. Familok: a typical working class house
5. Brat od Zosi (pl. Brat Zosi), Zosia's brother: here the German influence: Der Bruder von Zosia.
6. Tego nie idzie zrobić (pl. tego nie da się zrobić): again German influence: Das geht nicht zu machen
7. Szkrobać (pl. skrobać)
Features 5-6 are actually incorrect in Polish and the educated people avoid these expressions.
Perhaps the list is longer but I do not remember more at the moment. Generally, it is quite common to include some dialect words into standard Polish (Some more popular words which are sometimes used even by non-native Silesians are: 'ja', 'kiecka', 'hasiok', 'wyciepnóńć', 'fajrant', 'kołocz', 'modro kapusta', 'farorz', 'wodziónka', 'krupnioki', 'kopalnioki')