No Checkpoints will cause EXTREME problems for Xbox users, specifically the Xbox 360 users, seeing that the servers are below subpar and Often experience whole fire times getting booted to the start screen, and even getting disconnected from Xbox live, this WILL make the game even more frustrating for Xbox 360 players. As if slow loading menus and poor netcode was bad enough. You need to have checkpoints in or very little people will be able to finish it on the 360.
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I play on 360 and have since launch i never have issues with getting booted. It has to be your internet.