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Continuity: When John Travolta, Rene Russo, and DeVito meet at Martin's house, Rene and John arrive in their cars and park facing the wrong way (driver's doors toward the curb), which in Beverly Hills gets you a ticket, but when they emerge from Martin's house, Chili Palmer's van is turned around (and the BMW that Rene Russo was driving is gone) so that the automatic door scene can commence.
Other: When the guy is on the balcony, and gets shot over the rail, you can clearly see the top rail bend to let him flip over and fall. Then when he lands you can see what looks like the corner of a mat lift up and kick dirt up. The next shot shows the bad guys leaning on the very rail that just bent.