It holds up perfectly well and is still required reading for any serious inquirer of Greek Religion. It is now a bit dated, yes, it lacks depth in a few key areas (for instance, Indo-European religion in general), and it is a bit too heavy on the impact of the Near East in my opinion, but yes: still deservedly a revered entry. There are numerous newer entries into the bibliography of "Greek Religion" as a discipline, but none fully replace or refute Burkert Griechische Religion. Some others which are also essentially required reading (in random order as they come to me):

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Marinatos and R. Hagg (eds). Greek Sanctuaries: New approaches 1993, which is the definitive archaeological study. It should be coupled with:

de Polignac, Cults, Territory, and the Origins of the Greek City-State Chicago 1995 and then:

Alcock and R. Osborne (eds). Placing the Gods, Sanctuaries and Sacred Space in Ancient Greece 1994

Bremmer, Greek Religion 1999.

Haysom and J. Wallenstein (eds). Current Approaches to religion in ancient Greece 2011.

Larson Understanding Greek Religion: A Cognitive Approach 2016.

Buxton (ed.) Oxford Readings in Greek Religion 2000

Easterling and J. Muir (eds). Greek Religion and Society 1987

Hägg (ed.) Ancient Greek Cult Practice from the Archaeological Evidence 1998

Gould “On making sense of Greek Religion” in J. Gould, Myth, Ritual, Memory and Exchange. 2001.

Burkert Homo Necans: the anthropology of ancient Greek sacrificial ritual and myth 1995

Osborne “Hoards, votives, offerings: the archaeology of the dedicated object” in R. Osborne (ed.) The Object of Dedication 2004 (I think)

Pulleyn Prayer in Greek Religion 1997