I think the answer is that this is not a native speaker. Another possibility: some native speakers do this as part of their accent - mostly in the UK, I think, which is funny since they don't pronounce R's when there actually are R's.

there's no r after saw and there is no ya the record is lame

In linguistics, this is called intrusive-r. A net search will give you plenty of information.

1) It's not a native speaker. 2) Pronouncing "saw" like "sore" is a fairly common speech pattern in some parts of the US, and sometimes is a personal mannerism. 3) I don't understand your second question, but he is saying "I actually saw a dog in his window on Tuesday."

Like Dan said, it's not a native speaker. The cadence is also slightly atypical. In the US, also, there are some native dialects that say 'sawr' when they say 'saw.' Others may say 'sawl' when they say 'saw.' For understanding dialects, it can be difficult, especially without context. In real world conversations, we tend to have more context when deciphering speech.