Other mistake: When Eugene discovers that it really is Blind Dog Fulton, he (Fulton) says that he needs to get out to help Eugene find that lost song. Eugene says that he will be here at "5:00 a.m." When they breakout - which took all of about maybe 10 minutes, it's very light for the morning time. Looks to be maybe 6:30 by daylight savings time.
Suggested correction: Aside from the fact that daylight continuity is seldom strictly observed in any film, you should be aware that dawn on the East Coast visibly begins breaking over the Atlantic at around 4:30 to 5:00 AM during Daylight Savings Time. The sun may not have cleared the horizon, but the sky is really quite bright in New York City (and the whole East Coast) by 5:00 AM.
The time of sunrise varies and, although it isn't pointed out what month they left the nursing home, it is suggested that it was during the academic year - not a summer month when sunrise would be within the earliest time frame. Astronomical, nautical and civil twilight (all 6° or more below the horizon) do not radiate the amount of light shown in the movie. Moreover, it did not appear to get lighter out as they traveled, suggesting they departed after daylight, which would be well after 5 AM.