After escaping from the renegade general's compound, Hawke can be seen starting up Airwolf while wearing the gray flight suit. But when he lands at Eddie's trailer, he's wearing jeans and a shirt.
Near the end of the episode Stringfellow Hawke tells Roche to launch a "Falcon" at the about-to-launch nuclear missile but Roche presses a button clearly marked "Copperhead". The AIM-4 Falcon AAM (air-to-air missile) was the first AAM to enter US Air Force service in the 1950's but was rapidly replaced by the AIM-9 Sidewinder after its extremely poor combat performance over Vietnam and it would definitely not have been carried by Airwolf in 1984. The M712 Copperhead is a laser-guided 155mm artillery round and as such would be impossible to fire from Airwolf.
When they are pulling up to drop off Eddie, a news broadcast talks about the nuclear explosion and then says "In other news from Washington, your taxes are going up." As of the September 1984 air date, the amount of income to reach the maximum 50% taxation rate was $162,400, up from $109,400 in 1983. The minimums were raised for lower incomes as well. This means overall taxes were lower. Under President Reagan, the maximum rate of 50% was reduced to 38.5% in 1987.
When String rides the motorcycle to Airwolf's cavern, during the Airwolf start-up sequence you can see him sometimes wearing the Airwolf flight suit and sometimes wearing the blue shirt and blue jeans he arrived to the cavern wearing.
When Hawke is discovered trespassing and runs from the Jeep and helicopter, his sunglasses fall out of his shirt pocket onto the road as the shooter in the helicopter fires at him. When he raises his hands to surrender a moment later, his sunglasses are in his shirt pocket.
Near the end of the first season finale "To Snare a Wolf" it was revealed the Airwolf helmet visor would come down almost instantaneously when a bright flash was detected to protect the wearer's eyes. When Airwolf blows up the nuclear missile setting off the nuclear warhead, the nuclear blast flash is much brighter than the ones from the B-52 bombs in "To Snare a Wolf" yet the visors on the helmets do not automatically come down in this episode.
The missile shown at the camp would not have the range to reach their intended target of Moscow in Russia. Moscow is about 6,000 miles from Southern California.
An intercontinental ballistic missile would not launch with an armed warhead, so the nuclear detonation shown would have been impossible.