Factual error: When Lorelai arrives at the hospital, Rory says she is xeroxing a report that she needs to fax for Sherry because Sherry didn't make enough copies. No matter how many people the report needed to be faxed to, only one original copy would be needed.
Character mistake: In this episode, Rory tells Lorelai that she was cleaning her computer's hard drive because it was full of unopened downloaded files which were consuming her CPU speed. This is wrong, the situation which she's explaining would not use up any extra CPU speed - she may be trying to say her hard drive was extremely fragmented which MIGHT consume some CPU speed (but a tiny amount).
Revealing mistake: Rory and Lorelei stop looking for a place to carve their initials on the Chilton steps because they hear someone coming. A man walks by and his footsteps stop so they continue, but when the screen goes back to Lorelei you can see the man hiding in the plant behind her on the right.