In evaluating size, some doctors actually measure the height of the womb (fundal height of the uterus) by feeling through the prospective mother's skin. One low-tech way of doing this is to assume the fundal height reaches the belly button (umbilicus) at 20 weeks, and is either a week more for every inch above it (about the doctor's finger width) or a week less for every finger counted below it. In other words, if the fundal height were two finger-widths above the belly button, this would correspond to 22 weeks. In my experience, this somewhat cruder measurement method isn't any more inaccurate than measuring with a tape measure.
One of the two major problems during the second trimester is an incompetent cervix. Around 20 weeks is the most famous "fright zone" for this complication. An incompetent cervix just doesn't have the strength to stay closed any longer, so it dilates painlessly (without contractions), leading to a premature delivery. Since prematurity is one of the most costly medical complications there is, any patient at risk should be evaluated during this high-risk time. (Even when a cerclage has been used, this is the time when a baby has attained a size to put stress on it.) Sometimes prolonged bed rest is necessary as well.
This is the second major problem during the second trimester, also occurring at about 20 weeks, if at all. The placenta (after-birth) has usually picked a permanent spot during the second trimester, the rest of the uterus expanding away from its site of implantation. But if that site is over the exit route of the baby (over the cervix—on the inside, called the "os"), the placenta now blocks the only natural way out for delivery. In addition, as a highly vascular organ that can tear away ("abrupt") as the cervix thins and cause hemorrhage, the placenta also now endangers both mother and child. This abnormal placement of the placenta is called a "placental previa," or "coming before." The second trimester is the usual time for a previa to abrupt, and the timing couldn't be worse.