Continuity mistake: When Jerry goes to the door, you can see the telegram is by the letter box and after reading the telegram, he throws it away and jumps for joy. But when Jerry goes to show Tom the telegram, it is now back in its original position.
Continuity mistake: When Jerry is at the letter box when Tom is reading the telegram, you can see there is nothing by Jerry's feet. But when we see him a little later on, the envelope in which the telegram was sent in appears from nowhere.
Continuity mistake: When Tom is shocked to see Jerry in his car, he has a cigar in his mouth. But when he goes to look at Jerry in the next shot, the cigar has gone.