Can't read the disc
If this happens when you try to start the disc then it means critical data could not be read. Be sure to check the usb cable to the drive and its connections, and if you are using a different cable try swapping back the original to test with. To verify the connection try playing a DVD: if that doesn't work either then it must be a connection issue. If the DVD test works, try a different HD DVD. If that works then something is probably up with the disc, so try cleaning the disc. The Xbox player is pretty good at recovering from read errors once the movie starts, but read errors in critical areas of the disc used to start it up will cause this error.
Playback stops with an error code
If the movie starts up then dies with an error blade, note the error code (which is an 8-digit hex number). Try again and see if the problem is consistent. Error codes are caused by either bugs in the content on the disc, or by bugs in the player software itself. For player bugs, be sure you are running the latest version of the firmware (see below). Once you have confirmed you are running the latest player and the problem persists, then try searching the internet (or looking on the title-specific post that follows this one) for the error code and the title name which may lead you to a work-around.
Playback Hangs on startup (on network titles)
If the player appears to hang with a black screen on startup (but pressing Display still works), and it is a network-aware title then you may have hit a problem with the downloaded content. If other discs work but this specific one does not, then this is likely the problem. First be sure you have the latest version of the player (see below). If the problem remains then you will need to delete the pstorage for that title (see below). What can happen is that the downloaded content can be corrupt or have a bug, and the player will automatically run the downloaded content in preference to that on the shiny disc. Deleting the pstorage works around the problem.
Player Hangs after startup (or on non-network titles)
If everything seems to stop, press Display: if nothing appears then its a "hard hang" and the player has likely crashed: your only option is to reboot the Xbox. If Display works then it is a "soft hang": chapter skipping or pressing Menu may get you out of this state. The Xbox button then Y will exit to the dashboard if the title refuses to continue. Such issues are rare, and can be caused by a title bug or player bug. Be sure to be running the latest version of the player (see below). If the problem is reproducable I recommend searching the net for possible work-arounds, or report it to Microsoft.
If you are having trouble accessing networked content on a title, first off make sure you are signed into Xbox Live before starting the disc. This ensures you have a working network connection, and is a requirement before using any network features on the Xbox player. Next ensure Networking is enabled in the player: run any HD DVD disc, press Display, navigate to Network Settings and make sure Enable Network Access is checked. Additionally many network titles check the connection right when the disc starts up, so if you are not connected at that point then the network features will remain disabled. Second, be sure you are running the latest version of the player (see below). If this is all true but you still cannot connect to the networked content, check the support site for the disc you are using (many of the network error dialogs will include an error code and a web address to check for more assistance). As a last resort you may need to delete the title's pstorage (see below).
Make Sure You Are Running the Latest Version of the Player
The current version of the Xbox player software is 2.0.5127 (to see the version play any HD DVD, press Display then choose the ? icon). If you don't have the latest version then connect to Xbox Live and play an HD DVD disc to automatically update the player, or download the CD-R image and burn yourself an update disc. Note that player updates are separate and indepdent from Xbox Dashboard updates.
Persistant storage (or pstorage) is 192M of flash memory in the Xbox HD DVD drive that is used to store files for titles. There is a common area, an area for each studio, and an area for each title. Titles and studios are preventing from accessing each others areas. (As you may guess, each "area" here is really a subdirectory). Things that titles commonly store in these areas are bookmarks you have made and network downloads. To manage pstorage you need to go to the Xbox dashboard, go to the System blade, select Memory, then select HD DVD Player. You will see a list of title areas, along with their size. If you are lucky you will see an actual movie name, and you can select it and delete its pstorage. However many titles right now will show up as "Unknown Title", so to delete one you will need to guess which is the one you want to delete. It so happens that the most recently created title area is usually the last one one in the list, so try deleting that, or choose one based on the size: if most are tiny but one is many megabytes, chances are good that the large one is the network download. If this trial-and-error method does not work then you may need to delete everything from pstorage, which you do by stopping at the "Storage Device" screen, navigating to the "HD DVD Player" item and pressing Y for Device Options, then "Delete All Content". This will wipe every title's pstorage, so be aware of that. (The fact that many show up as "Unknown Title" is a problem that is being worked on: as newer titles appear which label their areas correctly, this problem should lessen).