From RFC 1035:
Authoritative Answer - this bit is valid in responses, and specifies that the responding name server is an authority for the domain name in question section.
So, what happens if this bit is set in a DNS query (QD=0)? Do most DNS implementations treat the packet as invalid, or would the bit simply be ignored?
The same question applies to other bits that are specific to either queries or responses, such as setting the RD bit in a response.
My guess is that these bits are simply ignored if they aren't applicable to the packet in question, but I don't know for sure or how I would find out.
I'm asking because I'm writing my own DNS packet handler and want to know whether such packets should still be parsed or treated as invalid.
You either apply the Postel's law ("Be conservative in what you do, be liberal in what you accept from others") - which is often touted as one reason/condition of the success of interoperability of so many different things on top of the Internet - or if you strictly apply the RFC you deem it as invalid and you can reply immediately with FORMERR for example.
In the second case, as you will get deviating clients (not necessarily for your specific case, in the DNS world they are a lot of non conforming implementations on various points), you will need to define if you create specific rules (like ACLs) to accept some of them nevertheless because you deem them to be "important".
Note that at this stage your question is not really programming related (no code) so kind of offtopic here. But the answer also depends what kind of "packet handler" you are building. If it is for some kind of IDS/monitoring/etc. you need to parse "as much as possible" of the DNS traffic to report it. If it is to mimick a real world DNS resolver and just make sure it behaves like a resolver then you probably do not need to deal with every strange deviating case.
Also remember that all of this can be changed in transit, so if you receive some erroneous things it is not obviously always an error coming from the sender, it could be because of some intermediary, willingly or not.
To finish, it is impossible to predict everything you will get and in any wide enough experiment you will be surprised by the amount of traffic you can not undersand how it comes to exist. So instead of trying to define everything before starting you should instead iterate over versions, having a clear view of your target (parsing as much as possible for some kind of monitoring system OR being as lean/simple/secure/close to real world features for DNS resolution as possible).
And as for "how I would find out." you can study the source of various existing resolvers (bind, nsd, unbound, etc.) and see how they react. Or just launch them and throw at them some erroneous packets like you envision and see their reply. Some cases probably exist as unit/regression test and some tools like ZoneMaster could probably be extended (if not doing those specific tests already) to cover your cases.