As I noted last week, the jump in claims was bogus, the result of flawed seasonal adjustment assumptions. This week claims fell by more than they rose last week, so claims are back on their declining trend.
At this rate, it won't be long before we see claims fall to 300K per week or a bit less, and that is about as good as it gets for the labor market. The most important thing that claims tell us is that there is no sign of any deterioration in the labor market, and therefore a recession or even a signficant slowdown in growth is very unlikely.
One of the most significant trends in today's labor market is the decline in the number of people receiving unemployment insurance. That is down by over 19% in the past year, or 1.24 million people. This is a powerful trend, since it creates incentives for large numbers of people to seek out and accept employment. Many have no doubt been discouraged in this effort, however, as witnessed by the very weak growth of the labor force—millions have simply "dropped out" and decided to stop looking for a job. But many of those are likely still on standby, ready to re-enter the labor force should job opportunities and other incentives to work improve.