A spechits overflow occurs when any single player or monster crosses and activates more than 8 linedef specials simultaneously. "Spechits" stands for "special hits" and refers to the number of linedef specials that have been "hit" by a player or monster after activating.
A spechits overflow occurs during demo playback when the array that stores the last 8 linedef actions trigger during that tic by a monster or player, cannot hold any more data. This results in any further linedefs specials from being triggered, as well as other linedefs not being checked. Ultimately this can lead to demo desyncs with players or monsters passing through impassible linedefs and such, or vital linedef specials to not be triggered to allow progress through the rest of the level.