There are potential issues with being in H-1B1 status and applying for a green card but they revolve more around timing - so, for example, if you entered the U.S. on an H-1B1 visa (as opposed to H-1B), which is not a dual-intent visa, then you would need to wait some unspecified period of time before applying for a green card to avoid being "charged" with immigration fraud at the time of your entry in H-1B1 status. Also, after filing your green card application, while you could continue working on your H-1B1 visa, you wouldn't be able to travel internationally on it and you wouldn't be able to travel in general for an extended period of time unless you had a family emergency abroad.