My husband was here on an L-1, and came and went as often as he liked on that L-1 until he applied for a Green Card.
Once the Green Card process was rolling he had to have Advance Parole (a piece of paper that says "you can leave the country") at all times when going back and forth to the UK.
He applied for his AP papers in December; they had not arrived by April, when we had a trip to the UK planned for Easter. He called the INS hotline (these are the heady years after 9-11), and he was told by the INS service desk that he did not need AP paperwork to enter the country because all his information was in the system and his receipt (piece of paper telling him his piece of paper was in process) should suffice.
Upon returning from the UK we spent 5 hours in the "Special" office at IAH because he did not have his piece of paper, just the receipt. It seems he had been approved for the Green Card but not informed; his AP papers were not in process since he had a Green Card "in the system." Border Patrol lets him in "provisionally" thanks to my pleading that he had no home in the UK, owned a home and had a job in the US and sending him back to London would be a great hardship to me as a citizen! His case was referred to Houston INS.
INS Houston officials refused to hear his case, told him he was going to be deported, and generally just wouldn't read the paperwork or take the time to try to figure the mess out. They didn't believe that he had been told it was OK to travel, "oh there's nothing we can do, the rules are strict now," yada yada yada. My favorite quote was "Well, at least you don't have kids."
After months of wrangling, many immigration lawyers, etc. his Green Card approval was REVOKED, he had to put in a new application at no cost to us, and he received a NEW Green Card approval in a couple of months. Serious money was spent by his company, serious hassle was what we went through and it was a nightmare. In the end it all hinged on the IAH immigration officer putting a stamp in his passport that fateful afternoon showed they knew he had a Green Card approved but he crossed it out and wrote "not valid for travel." His company also lodged a formal complaint after having another foreign employee who called the INS service line and got the same answer my husband did; apparently there were a few people at the INS who didn't know the rules and who were giving out bum information.
My husband received a letter of apology from three officers of the INS and in the end lots of people came up and apologized personally for so many mistakes on the part of INS. When we went in for the final "interview" the guy was totally confused by his file and actually had a big "REJECTED" stamp ready to go on his desk because he'd looked at the file and freaked out (he told us this), but the apology letter was stuck on the bottom of the file (literally last page) and when he read that he stamped us "APPROVED."
Moral of this long story: if you're waiting for your GC make sure you don't have to have your advance parole letter, and when they tell you it's not necessary check again. Urgh.