A professor at the University of Southern California gave Bryan Cranston lessons in chemistry basics for the series, so Cranston was able to correct some writer's mistakes. An actual DEA agent showed the crew and the cast how to make crystal meth. However, some steps were always omitted from the filming to avoid anyone using the show as a "how to" guide.
A plaque on the wall of Walt's home says he did research in proton radiography in 1985 that contributed to someone's Nobel Prize win. The winners of the 1985 Nobel Prize for Chemistry were Herbert Hauptman and Jerome Karle who won for their development of methods to determine crystal structures.
The show was originally planned to take place in Riverside, CA but was moved to New Mexico because the state offered an attractive tax rebate on production.
During Walt's surprise party, Hank stands up to toast and takes Walt's drink out of his hand to raise. This was Bryan Cranston's idea.
Bryan Cranston greatly impressed Vince Gilligan with the lack of vanity he brought to playing Walter White from the very first day of filming. His two major contributions to this were A) having Walter wear faded, stained, unflattering white jockey shorts and B) growing a very thin, pathetic mustache. Cranston later explained the reason for the former is that Walter was so miserable that even his underwear was pathetic and that the latter highlighted the pointlessness of his entire life because there was no point in even having a mustache if it was that wispy and embarrassing.