Note: if you are reporting a wrong signature of a function or a class in
the standard library, then the typeshed tracker is better suited
for this report: https://github.com/python/typeshed/issues

I tried that first ;-) python/typeshed#3805

Please provide more information to help us understand the issue:

• Are you reporting a bug, or opening a feature request?

This is a bug in the system overall but probably a feature request in mypy itself.

• Please insert below the code you are checking with mypy,
  or a mock-up repro if the source is private. We would appreciate
  if you try to simplify your case to a minimal repro.

from datetime import date, datetime
if datetime.now() < date.today():
    print("that's a surprise!")

• What is the actual behavior/output?

No error!

• What is the behavior/output you expect?

A warning, since at runtime I get TypeError: can't compare datetime.datetime to datetime.date.

• What are the versions of mypy and Python you are using?

0.770, 3.8.2

• Do you see the same issue after installing mypy from Git master?

Yes.

• What are the mypy flags you are using? (For example --strict-optional)

python_version=3.8
incremental=True
follow_imports=normal
warn_redundant_casts=True
warn_unused_ignores=True
strict_optional=True
strict_equality=True
no_implicit_optional=True
disallow_untyped_defs=True
disallow_any_generics=True