Shia LaBeouf Enjoys Sightseeing Day at Vatican With His Dad, on Video

Shia LaBeouf had a grand time exploring Vatican City in Rome with his father ... despite some outbursts in Italy during his trip for his dad's baptism.

See it for yourself -- you can see the actor exuberantly taking in the HQ of the Roman Catholic Church with his dad, Jeffrey, who is in a motorized wheelchair. Shia is as happy as can be observing the ornate artwork throughout ... even lying on his back at one point to get the perfect shot of a ceiling. There's more -- it's all in the clip.

As we've reported, Shia traveled to Italy for Jeffrey's baptism after a New Orleans judge granted him permission to travel following his battery arrest during Mardi Gras in February. The approval came after another judge originally denied his request to travel abroad between March 1 and March 8.

We're told the father-son day at the Vatican was in preparation for the baptism.

Though he looked like he was having the time of his life with his dad ... Shia's trip hasn't been completely smooth.

We broke the news -- he was spotted in his underwear in a hotel lobby in Rome ... seemingly frustrated no one would light his cigarette.

He was also seen clearly agitated with a woman sitting next to him at a cafe ... at one point even telling her, to "F*** off." He was later yelling in the street ... though it's unclear if it was directed at the same woman.

He has since returned home ... and even had another incident involving police at his New Orleans pad. We obtained video of the ordeal that shows him frantically telling officers to look at the security cameras at his home because he's a "target."