I have learned in school that letter 'r' is not sounded in the word 'considered', here's an example.
But I have been watching the 'How I met your mother' series, and Ted have pronounced that with sounded 'r', like this.
Is it some kind of mistake/difference between accents?
Most varieties of American English are rhotic. This means that speakers pronounce orthographic (written) 'r' regardless of the sounds around it.
In non-rhotic varieties of English - such as Southern Standard British English - orthographic 'r' is only pronounced if followed by a vowel. It doesn't matter if there is a double /r/ or not in the orthography:
car / ka:
car park / ka: pa:k
car alarm /ka:r əla:m
carrot / kærət
racoon / ræ'ku:n
In the sentences above the 'r's in car and car park aren't pronounced becuase they're not followed by a vowel. In contrast the first 'r' in car alarm is pronounces because it is followed by the vowel at the beginning of alarm. The 'r's in carrot and racoon are also pronounced for the same reason.
The Original Poster is obviously learning about a non-rhotic variety of English, maybe RP. However, the American speaker in the clip they are listening to speaks a rhotic variety. The Original Poster would expect the 'r' in considered to be silent because it is followed by a /d/. However, in the rhotic speaker's English it needs to be pronounced.
At least in the central u.s. the "r" is very clearly pronounced.
