Hi,
I'm the firmware update guy at HP, which is why I was drawn to your post, not the wireless guy, but I'll try to offer some helpful suggestions. I know these might not be anything groundbreaking. And sorry that our manual download software isn't smart enough to tell you the firmware is up-to-date, rather than just reporting an error. I wish I could give you a reason for why that functionality isn't in place.
Anyways, looking at the WIFI issues, you might try:
1. Set up a manual static IP address for the printer and the router.
Go to wifi->settings->advanced settings->ip settings->press OK on the warning if one appears->manual.
Then set up the stuff up. IP address could be like 192.168.1.150. usually subnet mask is 255.255.255.0, default gateway is usually 192.168.1.1, and DNS address si usually 192.168.1.1.
Then you might have to go to your router and assign the IP address (192.168.1.150 ni the example above) to the printer.
2. Use wireless direct.
Go to wifi->settings->On with security.
You can then see the display name and password.
Basically this turns the printer into a wireless beacon and computers and devices can connect to the printer as if they were connecting to a wifi router. I admit this solution is sub-optimal as it requires you to disconnect from the current wifi router you are on.
3. Try a "restore networks defaults" in hte wifi->settings option and then reconnect.
Sorry if these aren't helpful. Maybe a wifi HP person might be more helpful.