Your goal here is to engage your intuition in ways that will help you assess your own, written work. (Everything in this answer applies to your dialogue, but also to all your writing in general).
Our intuitions sometimes work in surprising ways. You can get to understand this process to some extent, but never completely, so it's good to 1) have some standard tricks to use, but also 2) try new exercises on a hunch, to discover what works for you.
Compare this to how we communicate to the reader. For instance, "show don't tell" is all about engaging the intuition. "Telling" provides some information directly, requiring very little processing on the reader's part. So, the reader's intuition is not engaged. "Showing" provides this information indirectly, often subconsciously, and the reader's intuition is engaed in order to process it. In the latter case, the information sinks in more deeply, and is subjected less to disbelief caused by conscious awareness that this is just a story.
How can you do something similar for yourself?
Start simply by reading your dialogue out loud (and, for that matter, your entire story): read it to yourself. Next, you may not have a writing group, but find a willing friend and read it to them--you don't even need to ask for feedback.
I found reading to a friend to be radically different from reading out loud on my own. As I read to the friend, my intuition was suddenly engaged, I was "identifying" with the "experience" of my listener, and suddenly I was much more critical of my words, more sensitive to the effect they would have on an audience.
There are more tricks.
Use a TTS programme (text to speech) to have your computer read your text to you. This engages your intuition differently, and provides you with a different point of view of your work.
Post a chapter of your writing online. With the work being "out there", suddenly you yourself will see it differently. Re-read it on the website where you posted it.
Read a chapter you have written, trying to select a single page or paragraph that you will read to a friend or post online for critique. Thinking about what selection to make will engage your critical thinking and give you a new point of view.
Write a pretend sales pitch to a publisher, where you praise your own writing and provide a sample of it (I'm not saying this is actually a good way to pitch writing to a publisher). Incidentally, I myself hate sales, so it is painful to do this. But, once more, new point of view, new way to engage the intuition.
Write a story in a story. The characters in the "outer" story tell eachother an "inner" story. Have different characters in the "outer" story respond differently to the dialogue in the "inner" story.
Re-write your text, changing between 1st and 3rd person PoV, but using the same dialogue.
Get a friend to read your text to you.
Having said all this, getting feedback is extremely valuable. If at all possible, try to do that too, when you and your writing are ready to move on to that stage.