As with other answers, I will say that the real "trouble" you can get into is limited to missing your flight and all the complications that can result from not being on the flight. Once the doors are closed, it's nearly impossible to get on the airplane (i.e. to get them to open the doors again). Not being there 30 minutes early also limits your ability to hear announcements about the flight and/or take advantage of situations which exist (e.g. on a lightly booked flight you may miss changing seats to an unoccupied row, as people who were there early may have already done so, with none left for you; on an overbooked flight you won't be able to volunteer for additional compensation to be bumped to the next flight).
In addition, when the flight is overbooked, passengers who are not present may be bumped without volunteering. When exactly that happens is, usually, up to the gate attendants. If you are not present when it happens, you will have no say in the matter. Usually, this won't affect you, but you have no input into the situation, let alone control of it, if you are not present.
What's printed on your ticket/boarding pass is what the airline is agreeing to as part of your purchase. If you don't comply, then, at a minimum, you have much less standing when requesting resolution after missing the flight. In fact, for non-refundable tickets, it's likely the airline will take the position that you didn't live up to your side of the contract and provide no compensation or rebooking (i.e. you'll have to purchase a new ticket for a later flight at the the currently available rates). What actually happens can largely depend on your relationship with the airline (e.g. frequent flier status) and how the agent at the gate/booking desk feels about you (i.e. be nice, polite, and ask for assistance; you can always get pissed-off later).
Do gates close earlier than what is stated on the boarding pass?
In comments, you've asked multiple times "do gates close earlier than what is stated on the boarding pass". The answer is that airline personnel usually wait until after the printed time to close the doors. However, yes, sometimes the doors are closed early. When the doors actually get closed is up to the flight crew and gate attendants.
My personal experience is that it's possible to miss your flight, even if you arrive 30 minutes early. I've had one flight where I arrived more than 30 minutes prior to the scheduled departure, but the plane had already departed. This happened with a major airline, at a major airport, but with a small airplane. The airline acknowledged the plane departed early, but gave no explanation as to why (or at least I don't recall them giving an explanation). They did re-book me to the next available flight, which was the next day at the same time. Needless to say, I arrived quite early the next day.