At 24:32 Adams is holding a pen in her left hand which instantly changes to an envelope in the next shot.
The patient (character Joe Reese played by Jake Weber) wears his wedding ring during the MRI. It is unlikely that House's staff would have allowed this as it could interfere with the results and be magnetically sensitive.
Immigration officers do not make house calls when doing interviews for those spouses applying for permanent residency permits (green card).
House mentions that Dominika made a trip to Bosnia. Her character is from Ukraine, and not yet being a legal permanent resident alien, if she had gone outside of the country, she would not have been allowed back in, and her application would have had to be started again from the very beginning. Being outside of the U.S. it would take about one to two years for her to have been able to return to the country.