1. The unemployment rate IS effectively zero. The vast majority of people unemployed today are either unable to work or have no interest in working.
2. That's a good point about "labor shortages" by sector. I agree with you for most sectors, but what you're overlooking is that many sectors are competing for the same labor -- and collectively there actually may be a shortage across multiple sectors. I wish truck drivers could be paid as much as medical doctors, for example ... but if that were the case then there would be a "shortage" of medical doctors as many of them change careers.
Such people are not counted as officially unemployed. Only those actively seeking work (have applied for jobs in the past 6 months) contribute to official unemployment stats.
This is a strawman argument, because there isn't much cross-sector competition between skilled, unskilled vs. professional workers, except perhaps in times of economic crisis when the unemployment rates is in the double digits. The issue at hand isn't that truck drivers are paid less than medical doctors - the issue (which is a problem from the standpoint of management and pro-immigration politicians) is that American truckers demand American truck driver wages rather than Guatemalan truck driver wages, just as American computer programmers won't work for Chinese computer programmer wages.