Can acetylcholine leak away from the synapse and cause spasms?
The enzyme responsible for the breakdown of acetylcholine (Ach), i.e., acetylcholinesterase, rapidly degrades, and inactivates Ach in the synaptic cleft after release. This process is particularly fast, as the synapse has to be cleared of neurotransmitter for a next action potential to occur (Čolović et al., 2013). So no, Ach does not leak away under physiologiocal conditions (Fig. 1).

In fact, common cholinesterase inhibitors that lead to Ach buildup by inhibiting its degradation, do not cause involuntary muscle twitches (spasms) as side effect. However, they do evoke muscle cramps, but that is easily explained by the increased retention of Ach in the synaptic cleft, leading to prolonged muscle contraction. 


Fig. 1. Cholinesterase is active in the synaptic cleft. source: Health &amp; Fitness. 

Reference
- Čolović et al., Curr Neuropharmacol (2013); 11(3): 315–35