Charlie Brown's team is the home team, playing on their home field. Yet when Peppermint Patty gets to the field, she says that his team are the first to bat. Home teams bat last. This may be considered a friendly game, but they have a schedule, which suggests it is a league game.
It would be impossible for the garden plants and trees to grow at the quick pace that is shown in the special. Planting would have to be done in the fall or winter and growth would take from weeks to months in order to be fully grown by baseball season. Trees take years to grow after planting.
After Peppermint Patty insists that Charlie Brown's team bat first, Snoopy bats, then Linus, then Lucy, who hits a home run. As she is rounding the base path, she runs by a score board that shows five innings of runs for the other team, which hasn't even been up to bat. This may be due to the score board having not been adjusted since the previous game. The team names are listed as simply "US" and "THEM".
Schroeder's mouth doesn't move when says "A promise is a promise".
The baseball field more than likely belonged to the town where the Peanuts gang lived and it would certainly not have granted permission to plant a garden there.
Peppermint Patty says her team will face Charlie Brown's team twelve times: twice in April, three times in May, twice in June, three times in July, four times in August and once in September. That adds up to 15 times. But then again, as a straight D- student, math is not Patty's strong suit.