In one shot, Hawkins turns his American Express card upside down to read the numbers upside. However, in the next shot, you can see the back of the card, with the magnetic strip on the top, meaning the cards is right-side up, not up-side down.
When the fire engines show up to fight the fire at the library, the engines are numbered 54 and 154 indicating they are from station 54 yet all of the fire fighter clothing is numbered 77 indicating they are from station 77.
Fire Engines have their own fire pumps and water tanks, thus even without the use of a hydrant the engines would've been able to pump water for a period of time.
Around the six minute mark Allison tries to show Skylar how to access a website using an IP address. She enters 827.750.304.001 into the web browser which is an invalid IPv4 address.