I am a full-time real estate agent and I have lived in the this area over 20 years. The only bad thing that I know of is the traffic. The Veteran's Expressway (Suncoast Parkway) has helped a lot with north/south commuters, but the east/west highways can be challenging. There is a plan to open another exit at Lutz Lake Fern Road on the Veteran's Expressway, but it isn't planned to open before next fall. Also, I've been told by others that there aren't enough churches. Two new one's have been built within the last two years, so hopefully that is helping on that front as well.
I personally don't know of any bad areas in Lutz, but every city has its crime. The Hillsborough County Sheriff's Office has an interactive website where you can lookup crime statisics at
County Crime Statistics. Lutz also crosses into Pasco County, so this site won't work for those addresses.