Deep rook endgame riddle

In June 1979, two months after the super event in Montreal, a small double round-robin  tournament for four players was held in the small Dutch town of Waddinxveen near Gouda. The world-class players Vlastimil Hort, Lubomir Kavalek and Gennadi Sosonko were, as expected, dominated by Anatoly Karpov. Going into the final round, the World Champion had already secured victory with a score of 4/5, 1.5 points ahead of second-placed Hort.

In the Karpov-Hort game from the last round, White gained dynamic advantages out of the opening. Eventually he was able to transfer to a major piece ending with the far better pawn structure. In those years, Karpov was famous for his brilliant endgame technique, with which he achieved many technical victories even from positions with only slight advantages. Especially after the exchange of queens, Hort's position therefore seemed practically extremely difficult.

You probably know that you can click on the notation below to get a replay board, and start an engine there to help with your analysis.

So Karpov did indeed win the game and thus the tournament by a margin of 2 points over Kavalek, who managed to beat Sosonko. The positional rook ending after 27.Rxe3 has been analysed and commented on several times. Especially extensively by Jan Timman in "The Art of Chess Analysis" (Everyman Chess, 1997 org. 1993) and Tibor Karolyi in "Endgame Virtuoso Anatoly Karpov" (New In Chess, 2007).

Their conclusion is that Black should give up a pawn right at the start of the endgame (instead of 27...Re8) to save his position. After this missed chance White is on the verge of victory, the annotators find no errors or significant improvements on either side.

However, analysis with a modern engine shows that a surprisingly high number of mistakes were actually made by both players after 27.Rxe3.

Can you find some of the critical moves, or perhaps even all of them?