A lot, that required or semi-required jQuery before can now be done with vanilla JavaScript, however jQuery is still going strong with invoking code on sets of elements as well as cascading calls.
jQuery has been a fantastic library and deserves all the praise, however a lot of its functionality has made it by now into the language itself.
To answer your direct questions, I couldnt think of any "issues", at worst you download an additional 30 kilobytes (gzipped) but with today's mentality of megabytes and megabytes for websites, that really shouldnt matter much. As for advantages, as mentioned, JavaScript did take over a lot of functionality, but as direct advantages I'd consider aforementioned features. Additionally, there certainly is also still a lot of libraries/plugins which depend on jQuery.
Understandable code as one programs the controller logic entirely and exposes it without magical hidden behaviour nor framework version dependency.
With no framework caveats nor non-intuitive behaviour to lookup in obfuscated documentation.