There's so many I'm not sure where to begin. A few simple ones that most people believe about networking on the Internet that aren't true are:
1. Routing paths are primarily decided by path distance as the metric.
2. IP ownership is authenticated and therefore the global route table is deterministic and stable.
3. DNS traffic is always over UDP/53
4. DNS is controlled by the network. Related, split horizon DNS is reliable.
5. Domain registrars and the root nameservers are required to be contacted in order to get a DNS response for a given public domain. As a corollary, seizing domains or blocking DNS at the root is a sufficient method to block access to a site. Secondary corollary, a correctly configured and valid public domain is reachable from anywhere on the Internet that can make a DNS query.
A lot of these are true in /some cases/, or in the general case, but not in the corner cases. A lot of policy and court decisions about the Internet assume the happy path or the common case when dealing with situations where motivated actors may take actions outside the happy path to work around that court order. It is entirely possible to bypass public DNS to resolve a public IP on the Internet as long as it routable, regardless of what registrars or public (and root) nameservers say. (see: Pirate Bay and their shenanigans, also see Tor resolvers, see non-authoritative DNS resolvers, see host file sharing, see alternate roots, etc.)
A lot of policies within organizations, including those set by network admins, are based on a belief that systems in their network obey the things provided by their network, when in fact the client controls nearly everything about how it decides to interact with a network, and the network can only provide configuration as a suggestion or recommendation. There are very limited options for enforcing policy at the network level. There is no guarantee that any given client on your network is actually utilizing your local DNS resolvers or successfully will resolve split horizon DNS.
A lot of configurations in the world are based on trust in systems which are inherently designed in an untrustworthy manner, or which require additional configuration and technology to provide an external basis for trust. This has had consequences with far-reaching impact and will continue to do (see BGP hijacking).
DNS, except when using newer protocols and taking extra measures to authenticate responses, is easily intercepted and hijacked. It is entirely possible to capture queries and inject non-authoritative responses, including responses which claim to be authoritative at any point in the path the query traverses. This is actually commonplace in some regions of the world (see: China). DNS that is authenticated and encrypted doesn't traverse UDP/53.