What functionality did the "Augur Escape Hatch" contract have between the launch of Augur and the contracts transfer to a burn address this week?
The Escape Hatch was a function which could be called on the
Controller contract: https://etherscan.io/address/0xb3337164e91b9f05c87c7662c7ac684e8e0ff3e7#code
When called the platform would no longer be usable for ordinary purposes (All functions will fail), and several "emergency withdraw" function would become callable.
These functions allow an address to withdraw any funds (ETH or REP) that they had in the system. As an example here is the method to get REP out of a dispute crowdsourcer in case of emergency: https://github.com/AugurProject/augur-core/blob/master/source/contracts/reporting/DisputeCrowdsourcer.sol#L62