As someone who has lived in Tucson my entire life (and attended the U of A for undergrad), these claims do have some merit.
The weather is beautiful for half of the year, and hostile for the other half. Get used to hearing about how "it's a dry heat" as that's how everyone here justifies it; doesn't make it anymore tolerable. In the summer it's common to have lows in the 90s or even 100s, and during the monsoon season (about 6 weeks or so during the summer) we DO have substantial humidity.
We do have culture and diversity, just have to look for it. Most parts of Tucson tend to naturally segregate themselves, so you really have to explore the city to find diversity.
The public transportation here is a JOKE. Agree with this comment 100%.
Overall, Tucson is a blue city in a red state. Even as a blue city, most of the blue is located in close proximity to the U of A, and the city tends to get gradually redder and redder the further out you get.
The traffic and infrastructure here are ridiculously bad. It takes about an hour to drive from one end of town to the other. There are two major freeways that go through the city, but they aren't the most useful or accessible for all destinations.
Critters do happen. I live pretty far on the outskirts of the city, and we do have our fair share of scorpions, spiders (including tarantulas), and snakes. But we also have really cool wildlife like coyotes, javelinas, and bobcats. If you have a newer house or even if you just maintain a regular cleaning routine, you probably won't see many critters in or near your house.
Hope that helps! If you have any specific questions about the city or the university, feel free to ask me!