Mistake #1 - Misunderstanding the alien's current immigration status. Adjustment only works if the alien can prove that he or she entered the US with permission (what USCIS calls "with inspection") meaning that the alien talked to immigration officers at the border or airport and was allowed into the country. If the alien entered without permission, adjustment is not possible. Aliens who entered without permission must return to their home country and seek a waiver of inadmissibility - a much more difficult and uncertain process.
Mistake # 2 - Believing that a marriage certificate is enough. It's not. Marriage to a US citizen doesn't give an alien any immigration status - it only provides a basis to apply. You have to prove a lot more to get your green card. You have to prove that the marriage is real and not just for immigration reasons. You have to prove that any prior marriages have ended. You have to prove that there is enough financial support available for the alien. You have to prove that you are not "inadmissible" because of past actions. If it sounds complicated - it is.
Mistake # 3 - Not telling the whole truth. The biggest mistake you can make is to lie or fail to disclose something on the documents you submit or in your adjustment interview. If your case is approved, the USCIS will forgive the fact that you overstayed your visa, the fact that you worked without permission, and even some minor criminal issues. But if you lie or fail to disclose something, the USCIS will deny your application. For the alien, that may mean removal from the US. Even the US citizen spouse is in jeopardy because lying to the USCIS is a crime.
Mistake # 4 - Moving. If you do not have a lawyer, the USCIS will send all notices to the address you give when you file. If you move during the application process, you have to notify USCIS. But in my experience, the USCIS has a terrible track record with address changes - they often continue to send notices and information requests to your old address - even if you file the required papers to change your address. If they send an interview notice or information request and you don't respond - they deny your case.
Mistake # 5 - Leaving the US. The 10 year ban kicks in when the alien leaves the US. Filing your adjustment papers does not change your immigration status or give you the right to re-enter the US. Many aliens are understandably eager to visit their home country after years away from home. Even though the USCIS has a way for aliens to get reentry permission while the adjustment case is pending, I strongly recommend that applicants stay in the US until they have their green card.
Mistake # 6 - Trusting that the USCIS will help you. They won't. The focus of many governmental agencies is to help people, but the USCIS is different. The USCIS will grant your adjustment of status application if you qualify and do everything right, but it is not there to help you along. It is nearly impossible to even ask them a question.