The Facebook Widget immediately force closes if you try to drag it onto any screen, but the main Facebook app works just fine.
I've had problems in Settings > Accounts & Sync trying to add Facebook to the list of managed accounts. I can select it from the "Add account" list, but it will not get added to the list of my synced accounts.
I've had some significant problems with the stock browser, namely that when I have many tabs open and use the Recent Apps button to toggle between apps, the browser will close and I lose all tabs.
Not actually unstable, but there are some quirks in the Honeycomb Android Market. I've reported the first two issues to Google, and have heard back from them that they are forwarding the first issue on to their Android Market Team:
1. The user's place in a long list of apps is not retained while toggling between the app list and app details. Example: Search on "Handmark" and the response indicates there are 134 matching results. Scroll down a couple dozen rows and touch any app to view the details. Now touch BACK to return to the list. Instead of seeing the same app you just touched, you are taken to row 1 and have to scroll down the list again to find the spot where you left off. (Not very convenient when you are browsing and comparing results!)
2. The Market Home page includes a link for "Android Apps for Tablets >" and below it displays 6 apps. If you click the link, the screen updates and you see 16 apps, but the header remains a link "Android Apps for Tablets >", but serves no additional purpose - it doesn't take you anywhere. Now search on "Tablet". It reports 1325 results were found. However, it only displays 19 apps and there's no way to scroll or see additional results - just these 19. So while using a tablet it's not easy to find tablet apps in the Marketplace app. (For comparison, the web marketplace reports 1399 results for a search on "tablet".)
3. In the Android Market on a phone you can rate a user's comment or report it as spam. I can't find equivalent functionality in the Honeycomb Market.
So my biggest problems really are not being able to add a Facebook widget and the Browser closing and losing my open tabs...