There are some things that are quite common in beginning cello pedagogy that I don't like much. The beginning bow hold with the thumb under the frog, for example, which teaches--for no good reason--a habit that has to be unlearned later. Another is the "left thumb as anchor," which teaches little hands to hit pitches chronically out of tune, and little ears to accept this poor intonation. I know why some otherwise good teachers are doing these things: because we all want to get a student set up with decent hand shaping so that they can advance to playing pieces quickly and not get bored and quit. But the fact is, poor setup leads to fundamental misunderstanding of how the body can be used to our advantage in playing the cello, and this in turn sets the student up for endless technical challenges later on.
It's not all doom and gloom, however. When I thought back to some of the exercises I was taught as a child, it seems that many of them make a lot of sense, even if children don't know what they're doing them for.