Private security guards and most certainly nuclear research employees are not allowed to carry firearms in the UK.
The Doctor is supposed to be looking over the plans for the building, but the screen is showing electronic circuitry rather than floor plans.
The administrator of the nuclear facility has a bug crawling on his forehead when he first begins talking over the loudspeaker.
The container in which Sarah keeps the hand functions like a classic magic trick, with the hand's performer hiding their arm through the bottom of the container and a false wrist applied to visible hand. The slice where the performers arm passes through is visible when the hand begins to crawl around (timezone 6:50 on the blu-ray release).
The film quality is significantly and noticeably worse when The Doctor is shown walking through the nuclear facility. Tom Baker clearly shot on location and the crew had to use lighter, handheld cameras with a different film-stock while in the facility.