Are there any downsides to these free certs? Do they work in all browsers; is there anything that could be better security-wise? If not, than this is exactly what we need to establish HTTPS as the new standard.
The cheap certs only offer domain verification; in other words, they verify that the person holding the certificate owns the domain in question. Typically via an automated email to one of the contact addresses associated with the domain. The catch here is that you're only allowed to fill out the CN= (domain) field in your cert; the others are blanked out. For what most people use SSL for, that's sufficient.
The more expensive certs will go a step further and verify the identity of the entity or person holding the certificate. This entails things like checking your articles of incorporation if your'e a business; things that tend to require a human operator at the CA reviewing your submission. In return, you get to fill out more fields in your certificate. However, nobody ever looks at the details for certs, so this is pretty much wasted money, IMHO.
The only point at which the more expensive certs get you something of value is:
1. You pay to get a wildcard cert, which lets you use your cert on as many subdomains as you want. If you actually need it for technical reasons (e.g. you let users create their own subdomains), this might be worthwhile. Most folks won't need this.
2. You pay to get an "Extended Validation" or "EV" cert, which gets you a little green box in the address bar with your company name. There's strict requirements on identity validation to get these, and it's supposed to engender more trust on the part of users. They're also very expensive. Personally, I suspect nobody really cares about these and it's just a racket for the CAs. But opinions vary.