Barney, BJ, and Baby Bop wear no clothes for the majority of the movie because they're dinosaurs

Barney changes Fig's diaper at one point during the movie and it appears he is naked but no private parts are seen.

None.

During the Fancy Restaurant scene, many people in the background are seen holding and/or drinking glasses that might have alcohol in them.

The circus scenes feature clowns which may be scary for those scared of clowns.

Much of the film has Barney and the kids going after an egg. Much of the people and things that get the hold of the egg nearly crack it in splapstick like ways but it might be suspenseful for younger viewers.

The climax scene where Barney and the kids ride a airplane might be suspenseful for its target demographic but for older people overall, not really that scary.