I have the same problem and the same issue; I can print (I do have a double-sided printing unit attached to the C6180, and there's a bug in the HP drivers that cause the second page to be printed upside down), but scanning and faxing is out.
I tried to solve it as follows: In System Preferences, I removed the printer queue for the C6180; then, I went to /library/printers and deleted the entire HP folder. Then I deleted all files pertaining to HP in /library/receipts. I reinstalled the software from the CD that came with the C6180; at some point, the installer told me to open the print center. Leopard doesn't have one, so I set up the printer using the Fax & Print section in System Preferences (my printer is connected via WiFi, and it shows up as a device under Bonjour). I was then able to configure the printer with the application that the HP installer puts into the dock.
This allowed me to print and scan, but not to fax. The only way to fax right now is to print out the fax and then send it by using the C6180 as a standalone unit. Scanning turned out to be a bit erratic and unstable; because I have an HP 5470 ScanJet scanner that works perfectly (after I manually re-installed its software; the scanner was no longer functional following the installation of Leopard), I decided to revert; I de-installed the HP 6180 software, then followed the steps outlined above to remove the HP items in /library/printers and /library/receipts. Finally, I re-installed the HP drivers from the Leopard installation DVD and added the printer through System Preferences -> Fax & Print.
HP is working on new drivers; in fact, beta drivers for the 5180, 4180, as well as a few other Photosmarts have already been posted by HP, so I expect a solution for the 6180 very soon. In the meantime, if you absolutely must scan, the above should work for you. If you do have a few days, you may be better off waiting for new drivers from HP. Either way, you can use the C6180 to scan in standalone mode.
Daniel