As many of you have noted, the Crimson Map Pack download for War Games Map Pass and LE owners has started rolling out. Reboot your console, load Halo 4, press Start, and select "Xbox LIVE Marketplace" to see if it's available for you.
The Crimson Map Pack should be available for download by War Games Map Pass and LE owners within the next two hours via the in-game store. To get to the in-game store, load Halo 4, press Start, and select "Xbox LIVE Marketplace". The DLC you want to download will be called "Crimson Map Pack (Season Pass)".
TL;DR - We are aware of the issue in which Map Pass and LE owners are not being recognized to download the Crimson Map Pack at no additional cost. We will use this thread to provide updates when we have them.
TL;WR - To prevent War Games Map Pass and LE owners from purchasing content twice, we created two different offers for the Crimson Map Pack, one that costs 800 MSP and one just for Map Pass and LE owners. The latter is currently having issues with showing up when appropriate, which is why some of you are not seeing a download for the Crimson Map Pack. We apologize for the inconvenience, and we're actively working with Xbox LIVE to have this issue resolved today. More updates when we have them.