Let me start off by saying I love the game. I am an ex-DotA player who got tired of the tedium of what was basically a PvE grind at the beginning of every match (last hitting / jungling). Demigod is a new take on the genre and I hope it continues to grow and improve. However, it is obviously not a perfect game. I'm going to list the primary problems I think it has, and welcome any contributions and comments.
High Alert
1) Connectivity issues - I will go out and limb and say this is the most important problem that needs to be fixed. As the devs have stated, there is no single host to this game and every computer must be able to host every other computer. These will either inspire people to make the necessary adjustments to their routers, or exclude a large group of people from anything but LAN play (some college dorms, for example).
Possible Solutions: I doubt GPG is going to go back and change the whole netcode, but we can mitigate a lot of these issues by adding some type of connection votekick. One player holding back a whole group of people by not being able to connect? Votekick 'em. I think the devs stated that they are already working on this. Other than that, we have to, as a community, be helpful in getting people setup with the correct settings for routers, port-forwarding and the like.
Medium Alert
1) Educating New Players - There is currently no tutorial in game. Though I don't believe this game is complex, I'm also looking at it from the viewpoint of someone who has played DotA for years. For many people, this will be their first dip into the genre, as this is the first full priced title of its kind. And let's be honest: This was the worst part of the DotA community. If you were bad at the game, you were yelled at. Players either quit, or forced to research tons of things by themselves and eventually picked up the same type of elitist attitude of "I learned before I started playing, and you should, too!"
Possible Solutions: A full-fledged tutorial would be nice, but I pretty sure that isn't happening. How about in single-player, there is an option for tutorial-tips that pop up? A new player can start an easy-AI 1v1 skirmish and tip bubbles could pop up around the interface, so a new player can get acclimated with the UI, at the very least.
Also, this is where the community has to step it up. We need to be civil and accomodating, both in game and on the forums. At the very least, we will need an active forum with an active strategy section, so we can point new players to a place where they can learn. If GPG can get new players familiar with the UI at the very least, I'm sure we, as a community, can come together and help new players the rest of the way.
Low Alert
1) Game balance - No game is every balanced perfectly. Ever. But nonetheless, this will always be a concern.
Possible Soltutions - As long as there are active updates by GPG, strategies and builds will fluctuate often enough so that the balance problem never becomes glaring and stagnant, and that's good enough for me.