After Picard talks to Riker and Troi about his career, La Forge calls him for a statistical analysis he's supposed to bring him, the analysis he was holding when he entered that reality. However, when Picard is walking to the Turbolift, despite asking to go to Engineering, he's not holding the analysis.
Due to the episode "Rascals" earlier in Season 6, Picard can't possibly have a synthetic heart after the transporter reconstituted him as an adult... or for that episode to work, for that matter.
When young Picard is lying bloodied on "heaven's" floor, the handle of the dagger that stabbed him can still be seen sticking out of his back but the dagger's corresponding blade is missing from his chest.
When speaking with Q in the afterlife, Picard claims that if he didn't have an artificial heart then he "wouldn't have died from a random energy surge thirty years later." In the cold open, it is established that Picard's artificial heart malfunctioned when he was struck by a weapon, not due to a random surge of energy. However, the actual event is not shown. If it was a surprise attack, and Picard was the first one hit, he may not have realized that he had been shot. An "energy surge" might be the only thing he perceived before losing consciousness.
As Picard chats with Q in the "afterlife", they pause their conversation and watch a visual recreation of the "young" Picard fighting with a bunch of Nausicaans. After the young Picard hits the first Nausicaan, he (the Nausicaan) falls backward and, as he hits the ground, his long black wig comes off. The Nausicaan then quickly rolls out of the camera shot, leaving the wig behind. (This all happens very quickly and is easier to see in slow motion.)
Picard tells Q that he would rather have lived his past life and die rather than the life he has from the altered time line. Although he prevents the falling out with Corey Zweller, he still left one of the altered events, which was him sleeping with Marta Batanides.
Picard mentions that he died 30 years after getting stabbed in the heart. While giving a toast hours before being stabbed, he says "Here's to the class of '27." The sections of the story that take place when he dies are set in 2369. 2327 would be 42 years earlier, not 30.
In the final scene, Picard laments that he does not know whether his experiences in time were real or if it was possibly an illusion he experienced near-death. It would be a simple matter to confirm it: contact Corey Zweller and Marta Batanides and ask how they remember the days leading up to their first deployment. If the events Picard experienced really were Q sending him through time, then Zweller and Batanides would remember the new sequence of events rather than the original one that Picard recalls. If they still remember the original version of history, then Picard did not actually make any alterations to history and his experiences with Q could be confidently chalked up to a near-death delusion.