Syntax checking (also known as linting) has essentially become a staple in any multi-person software project. There are many linter programs available online, which support different languages and styles.
Python code has it easier than many languages out there, as it tends to adhere to a single standard—PEP8 (https://www.python.org/dev/peps/pep-0008). The most common linters that make sure the code adheres to PEP8 are Pylint, Flake8, and autopep8.
Before proceeding, make sure one of these (the following examples work with Pylint) is installed on your machine, as Vim merely calls external linters.