The address referred to in the title is 1600 Pennsylvania Avenue, Washington DC, better known as the White House. When a female staff member is stabbed to death in a washroom, homicide dick Wesley Snipes catches the case. He instantly clashes with political factions close to the President (Ronny Cox), who is himself too wrapped up with a hostage crisis in North Korea to pay much attention. Chief of security Daniel Benzali - the Lex Luthor lookalike from TV's Murder One - narrows his cold eyes and saddles Snipes with Olympic gold medallist-cum-secret service woman Diane Lane as a liaison.
The establishment wants a fall-guy cleaner for the killer, but Snipes scents cover-up and suspects the Prez's studly son, who was having an affair with the victim. Meanwhile, prominent character actors in cameo roles do their best to seem suggestively innocent: Diane Baker is the First Lady, Alan Alda the national security advisor, Harris Yulin a hawkish general. The sleuthing peters out when it becomes obvious that yet another conspiracy is afoot, and Snipes and Lane get chased around town by the regulation sharp-suited hi-tech hit team. For the finale, our heroes have to perform the first successful penetration of White House security since the British torched the place in 1812, and break in via secret tunnels to avert more dirty deeds.
Though it might charitably be described as "a load of old cods", there is a certain entertainment value to Murder At 1600. Snipes jumps through the hoops smartly, and Lane, one of those actresses rarely well used, is smart and appealing as the secret service chick, showing off her gold medal skills (sharp-shooting) and finally performing a spectacular (if silly) bit of duty.
Incidentally, the conspiracy-minded might wonder why this and the similarly-plotted Shadow Conspiracy have cast Alda and Donald Sutherland, the two actors who played Hawkeye Pierce in M_A_S*H, as equivalent sinister White House staffers.