It's been a while since the last Ask Augustin! I get the question "how do you play cleanly" pretty often, and it is a difficult one to answer, because there are so many factors that contribute to what one might describe as a "clean" sound, or "clean" violin playing!
The most obvious are intonation and sound quality, that the notes are not only in tune but also played with a pure enough sound, without too much noise or distortion. I don't delve into intonation here since I have videos about that already, and wanted to focus on the other aspects of clean playing.
Just as important as the notes themselves is actually what happens between the notes!
The most essential part of working on a clean sound has to do with listening to yourself while practicing. It's easy to not even hear certain aspects of the sound, or shifts and noises between notes, because we are not expecting or wanting to hear them. The mind can play tricks on us like that sometimes and so we hear what we want to, not what really happens! This is why recording yourself during practice can be so useful. It can be tough to listen to yourself so closely and critically, but it is an important step in order to get closer to the sound you want.
Shifts between notes are one of the reasons why some players sound "cleaner" than others, even though both players might play perfectly in tune and with beautiful sounds.
When you have notes under a slur, it's important to work on your left hand so that the note changes are clear, and "clean" enough. Without getting tense, your fingers have to come down and lift up suddenly enough to create clean changes of the notes.
Finally, the coordination between right and left hands is essential for clean changes of notes when the bowing is separate.
One of the most counterintuitive things about playing the violin is that the left hand needs to move slightly before the notes are played (and the notes are actually played with the right). I've become really aware of this as I've worked on synchronizing videos over the past few months. The fingers of the left hand usually go into position slightly early before the note is actually played. Only in very fast passages does it look like it happens at the same time and yet, looking closely at a high framerate, the left hand still moves a splitsecond before the right in order to get clean note changes during fast passages. This is totally different from the piano, where you press a key and that's when you played the note.

I hope this gives an overview of what clean playing consists of. Each one of these aspects is quite a big subject!