Aside from that, I'd say that there are a few benefits over RSS:

1. It's faster to setup and start tracking something, as all you have to do is send us a tweet. This might work especially well for stuff you just want to track for a couple days, when setting up a bunch of search feeds is overkill.

2. A lot of people still don't use RSS, but use Twitter.

3. I tend to only check my RSS once a day or even every other day, while I'm likely to be on Twitter all day, so I'll see stuff more quickly than I will with RSS.

This is just off the top of my head...as I said, this is an experiment for us, so all feedback is useful :)

Doing it through Twitter DMs = not so much, imho.

Twitter just has way too much noise, so it's not a great interface for receiving alerts about important information. I'd rather get alerts via RSS or some sort of custom dashboard. Better yet -- offer the alerts as many different ways as possible: RSS, Twitter, web dashboard, iPhone app, email, etc. and let users use as many different alert methods as they want.

For my last job (community management at a startup), I had a ton of RSS feeds set up pulling in blog searches, Twitter searches, web searches, etc. on our brand. I also had email alerts set up, and a Twhirl running in the background on our Twitter account pinging me on @ replies. My goal was to make sure I had as many different ways to catch, filter, and alert on all that info as possible so I didn't miss anything important. (Something to filter out the redundancies would have been nice, fyi! :)).

Specifically, the twitter-less monitoring interface (e.g. a daily email) would make lot more sense. At least to someone who is not a Twitter user, but would like to track what's being said there about the product/company/etc.

Quick poll: if we added an email-only version of MightyBrand where you got a daily email of all of your social media mentions, would you use it? How much would you pay? $5 / month? $10 / month?

In this case I think a small account will be able to justify the $5 month. For the large accounts you can charge $100/mo and they will pay as long as the service in itself is useful.

(edit) Just checked your pricing - 24$/mo. Ehrm .. hrm .. well .. is it working well ? Especially since you are trying to sell the same service to the individuals and the enterprises. The enterprises will likely think it's not "enterprisy" enough, and individuals - that it's overpriced and an overkill for them. At least that's my guess based on what what 5 sec. impression was (and I am in the need of a such as service).

As to your 2nd question, Google Alerts doesn't track everything we track now, and tracks a small slice of what we'll be tracking in the next few weeks.

So why not create a site, where i can log and find my alerts?

This option is already available with Google Alert (have you tried it). It sends me daily reports of keywords mentioned on the web.