Pronunciation is definitely the biggest thing that people notice when you are speaking English.

Do not make this mistake! You have to remember that:

Your teacher has been listening to bad English for years. He or she can understand it much more easily than the average person.
Other students are usually from the same country as you. Therefore, they speak English like you and they make the same mistakes. So it is easy for them to understand you.

When you talk to a person in real life, they may not notice your limited vocabulary or grammar mistakes. But they will notice right away if your pronunciation is good or bad. If your pronunciation is poor, they will think about you as the guy/girl who speaks bad English, and good grammar and vocabulary won’t help you!