Is a 302 redirect to relative URL valid, or invalid?

RFC 2616 requires an absolute URI in the Location, but that standard has been replaced, since June 2014. The relevant specification is now RFC 7231. The relevant section of the new standard says:

Location = URI-reference

The field value consists of a single URI-reference. When it has the form of a relative reference ([RFC3986], Section 4.2), the final value is computed by resolving it against the effective request URI ([RFC3986], Section 5).

So a relative URI is now permitted. The effective request URI is the same as the request URI in most cases.

Relative URLs are valid.

There is a bug in RFC 2616. See http://greenbytes.de/tech/webdav/draft-ietf-httpbis-p2-semantics-17.html#rfc.section.9.5.