I don't think journalism degrees are all that relevant for critics. What did teach future journalists has little to with reviewing unless you count advice such as 'write often' and 'work on your language skills'. Besides, I prefer critics with a love for and a good understanding of the medium, and they don't teach that in school
As for the other positions: there's not that much to reporting the daily news since most of it comes straight from the developer/publisher. Sadly this a tightly controlled industry with little wiggleroom for investigative journalism. On the other hand, what would need to be investigated? Aside from the occasional screw-up from companies like Ubisoft there aren't many big things to report on. Don't get me wrong, it's great to go after stuff like that and publications certainly should, but you don't need a full staff of journalists for that.
Now that I think about it, most of the magazines and websites I have experience with have a journalists or two, but it's hard to tell them apart from the philosophers, engineers and college drop-outs. And when it comes to investigating it's usually the ones with the best knowledge of the industry and, of course, the best connections, that get the best info nuggets.
Anyway, to answer the topic question itself:
-Ideally I would see more advertisers from other industries. Critics are shielded from advertisers (in the case of magazines, we don't see who bought space until we open up the mag itself) but I know ads can be a major headache for editor-in-chiefs and whoever else happens to have to deal with advertisers. There was this one time I gave a game a bad review and by bad, I mean really bad. It deserved it. The publisher didn't like it and the mag lost their business. The editor-in-chief told me not to worry about it. I did my job and I did it well. Other people might give in to the pressure, though, so it would be best for everyone to look for ad income elsewhere. Easier said than done, sadly.
-Better pay for critics. For magazines you're usually paid by the page, regardless of the content. Of course, a review costs a lot more time than a hands-on/preview, so if you tend to write a lot of reviews, you may be working for less than minimum wage most of the time. While I know plenty of critics with strong work ethics and I like to see myself as one as well, it's very tempting to rush an assignment when you look at what you're actually being paid.
-More opportunities to play big titles at home instead of a controlled environment. There are two reasons not to like controlled environments. The first is that it might influence the critic. While most controlled environments are pretty basic (you're invited to come over to a publisher and play the game, sometimes for as little as 4-5 hours, while being served snacks and pop) some publishers go really out of their way to make it a good experience. Worst I've heard was several days in a luxurious hotel to play an online multiplayer shooter under perfect conditions (honestly can't remember if it was CoD or Battlefield). As fun as this all sounds, it's actually quite a hassle for most critics. Remember, they're still being paid by the page and so it sucks when they have to travel a lot in order to be able to play the game. Personally, I hate trips like that. I'd much rather play games in the comforts of my own home.
-Less embargoes. I understand why publishers want to focus publications of reviews around the release of the game, so I don't feel too strongly about pre-launch embargoes, but post-launch embargoes are complete bullshit.
-Kinder readers. Gamejournalism is partly the way it is because it's trying to live up to the demands of readers. We need to, because we need their attention (and in the case of paper mags: money) to stay alive. If readers are more understanding about reviews popping up a little later, publications can take a stronger stance against bullshit for publishers. Also, it be really nice if people stopped attacking the industry as a whole just because they've read about some bad apples. It hurts a little to go online in the morning, open up some feeds and see all sorts of posts about how critics/journalists are terrible people who don't deserve decent pay.