I get error messages like "multiple RRs of singleton type" and "CNAME and other data" when transferring a zone?

These indicate a malformed master zone. You can identify the exact records involved by transferring the zone using dig, then running named-checkzone on it.

CHARSET=ASCII IDN_DISABLE=1 dig +onesoa axfr example.com @master-server > tmp

named-checkzone example.com tmp

A CNAME record cannot exist with the same owner name as another record except for its RRSIG and the DNSSEC records which prove non-existence of other records (NSEC).

RFC 1034, Section 3.6.2 states: "If a CNAME RR is present at a node, no other data should be present; this ensures that the data for a canonical name and its aliases cannot be different. This rule also
insures that a cached CNAME can be used without checking with an authoritative server for other RR types."