The New York Times likes it, closing by calling it "pure, nutty fun." Time Magazine says it's "the very oddest good movie in many a full moon." The Variety review is here. 1000 Misspent Hours says it eventually achieved status as a cult film but that
its initial release was such a cataclysmic failure that it drove the Sherwood production company out of business, instantly scuttling the sequel proudly forecast in the closing credits and creating a thicket of ownership quandaries dense enough to send the VHS tape swiftly out of print and to delay the DVD release for years.
Moria opens with this:
The Adventures of Buckaroo Banzai: Across the 8th Dimension is an object lesson in how to create an instant cult film. Buckaroo Banzai fulfills all the requirements of a cult film – it is exceedingly eccentric, it was a commercial failure at the box-office, it instantly received a fan clique – all without it ever being a particularly good film.
2/18/2010: Great Old Movies calls it "a tedious and woeful, career-killing failure virtually devoid of entertainment value" and "virtually unwatchable".