Recruit friends to read your dialogue out loud for you. Unfortunately, novice screenwriters are often so protective of their work that they only read it silently to themselves. The problem with this is that practically anything can sound brilliant inside your head. If you have written long sentences that take two full breaths to deliver, involve tongue-twister combinations of words, or laughable phraseology such as "I just saw something move on Uranus", your ear will catch more goofs than your eyes.
Look at each page of your script. If it's a succession of one chunky paragraph after another, your characters are talking too much in speeches. Excessive speeches not only slog the pacing of the story but will also bore an audience because all you are giving them is a tennis game of talking heads. Break up those long speeches with interruptions and action. Strive for as much white space on each page as possible.
Circle every time a character is addressed by name. In normal conversations, people typically don't keep repeating each other's names to one another, especially if they're the only two people in the room. Unless the use of their name is for a specific purpose (i.e., an introduction, a warning, a plea, etc.), omit it. Seeing all those circles on a script will cure you of this common habit pretty fast.
Minimize the use of parenthetical directions on how to deliver a line (i.e., angrily, happily, sadly). If dialogue is written well, all of these adverbs are totally unnecessary, not to mention that they also eat up valuable line space if used excessively. The exception is if the absence of an acting clue would skew the intended meaning of the line (i.e., the way in which the line is said is contrary to the generally accepted interpretation of the words themselves).
Write foreign dialects in regular English rather than spelling everything out phonetically. Writers always think they are doing actors a favor by penning phrases such as "Pardone ay mwah but verr iz zah railvay stahzion". It takes time to decipher all of this gibberish when you could simply write "with French accent" in parentheses above the line and an actor would know exactly what to do.
Highlight all of the lines of any single character who speaks in a dialect and read them through as if they were one continuous monologue. This will help you determine if you have stayed consistent in their dialect, grammar and vocabulary throughout the entire script. Do this for each of your characters, especially if you have been working on a script for a long period of time; it's easy to forget their respective "voices" and have a character who started out in Act 1 saying "ain't" and "gonna" end up speaking the Queen's English by the final credits.
Eliminate superfluous dialogue that doesn't advance the plot, reveal new dimensions of character, or help resolve the conflict. You only have 95-120 pages to tell a complete story; don't waste it on "How are you?/I am fine/What shall we have for lunch?/Oh, I don't know/What do you want?". While these snippets of chatter run rampant in real life, the goal of crafting realistic dialogue for the screen is knowing when to eliminate all the filler that simply doesn't go anywhere.
Restructure any dialogue that only serves to explain things to the audience that the characters engaged in conversation presumably already know. Example:"Well, if it isn't my older brother Bob from Duluth who repairs pianos for a living and has been married 16 years to a Vegas showgirl named Alice. Hi, Bob!"If something significant needs to be conveyed to the viewers, find creative ways to do it that don't involve explanatory speeches.