Corrected entry: Robin walks into the apartment and sees a goat turd, which can only be there if The Goat was in the apartment. She goes on to talk to Marshall about keeping quiet about the fact that she slept with Barney, so we know that this happened when Ted was turning 30. But later in the end, Ted says that The Goat was actually there on his 31st birthday. So The Goat turd could not have been there at the time.
Correction: First, it's more like 20 years in the past (2030 is present and 2005 - 2013 is the past... Ted turned 30 in 2008). Second, Marshall threw 2 surprise parties, the first on Ted's 30th birthday and the second on his 31st birthday. It is totally conceivable that Present Day (Bob Saget) Ted co-mingled the events of two separate birthdays that occurred 22 and 21 years in the past; one where Robin identified The Goat turd (Ted's 31st birthday) and when Robin slept with Barney (Ted's 30th birthday) especially if the focal point in his mind was a surprise birthday party. Finally, that is the point of the end of the episode when Present Day Ted acknowledges that The Goat incident happened the following year so the viewer is meant to disregard any references to The Goat on Ted's 30th birthday.
Correction: This whole show is told in flashback from a guy remembering 10 years previously. It's the type of thing where it's very, very difficult to pinpoint what is a mistake and what would come under remembering, which I think this does. It would only be a plot hole if it meant something else in the series couldn't have happened unless it specifically had to be there on his 30th.
The_Iceman