At the hospital, Matt wears a light gray shirt with a button-down collar. When he leaves the hospital and gets into Elektra's car, he wears a glossier white shirt with no buttons on the collar.
When Elektra reads the Roxxon ledger in Japanese, she turns the pages and reads the text from left to right. Japanese texts are most typically written from right to left.
The flag on the back wall of the court room does indeed have 48 stars. However, there is another flag on a stand near the judge's bench., which is the correct placement for a US flag in a US court. This second flag is not unfurled, so there is no way to know how many stars are on it. The flag with the 48 stars is likely just set decoration.
When there are shots of the jazz band playing at the party, the instruments being played do not correspond to the song heard. For example when the trumpeter is playing, no trumpet can be heard in the song.
Castle asked Foggy to leave the room to speak with Karen alone. Without an attorney present, Attorney/Client privilege wouldn't apply and Karen could be called to testify as a witness on what was said in the hospital room. Therefore Nelson-Murdock would probably have to recuse themselves due to conflict of interest.