At today's mammogram, the tech mentioned I had high density in my breast and not to be surprised if I get a call to come back. Should I be concerned?

Common finding. Women in their 30s and 40s tend to have denser breast tissue. As such, it makes it more challenging for the radiologists to interpret. Often times, women are asked to come back so they can take more views and make sure they are not overlooking anything. It is not a cause for concern.
No, dense breasts are normal, but they can make the interpretation of the mammo more difficult, and there is a higher chance of getting called back for extra views to spread out the densities. The tech probably informs everyone that there is a chance they could be called back(mine do) so patients are not surprised/alarmed if it happens(which is about 10% of the time). 80% of the time it turns out ok.