When baby bear is shown running towards the house the diaper he is wearing is missing the knots that keep the diaper tied on.
In the beginning of the show, Pa Bear is shown reading a newspaper with a Bugs Bunny comic strip on it. It is later revealed that the newspaper he was reading was dated in the year 1928. This is ten years before the Bugs Bunny character was created.
The original newspaper with the want ad that the papa bear read is from 1928. In 1949 papa bear says their act is finally ready, 21 year later. In that 21 year span not one of the bears have aged or changed in appearance.