Continuity mistake: When Oscar is on his way into his building, his sweat suit is perfectly clean after playing baseball. Once in the apartment he is covered in dirt.
Scrooge Gets an Oscar - S1-E12
Continuity mistake: Watch the scene when Oscar opens his mini garbage pail gift. You'll see it's completely free of the inside tissue wrapping. In the next shot when he goes to open the lid, there's a piece stuck between the lid and the base that was not there before. (00:20:40)