If it really is the rom causing the problem the developer will probably issue a patch but it could just as likely just be a bug with the new market system in general, definitely isn't the first time google issued something buggy.
I haven't had a chance to try the web installs yet but will report back.

 

I have been running the Skyraider ROM for a while with no issues downloading. Today for the heck of it I was bored and decided to download the CyanogenMod ROM again and play with it. I have ran it before with no issues but today it would not download certain (most) apps from the market such as Titanium Back up. I didn't mess with it much though and just flashed back to my back up of Skyraider which has never failed me.

 

But he also stated he would fix any outstanding issues, but it doesn't look like it's a rom issue anyway because other skyraider users aren't having the problem.

 

AppBrain sees each install of a new ROM as a different phone, I'm wondering if the online market does the same thing.
In the online market click the 'My Market Account' link in the upper right hand corner, then click the 'Settings' tab. Do you have more than one phone listed? If so, make sure the 'correct' one is shown in menus.

Edit: here's a link to another discussion on the new market.
http://androidforums.com/android-lounge/270327-market-webstore.html