All outstanding transactions are verified/cleared each time a block is generated. On average, a block is generated roughly every ten minutes. Transactions are small enough that even if Bitcoin becomes as popular as PayPal, the amount of space required will remain reasonable and the rate of increased space required will be less than the rate that average hard drive size increases.
"Will be less than the rate that average hard drive size increases"
Woo, that's fantastic. Betting the entire system's space feasibility on the disk equivalent of Moore's law...
In other words, you're assuming that the rate of increase in storage space will not wane...which may be realistic, given recent advances in quantum computing, but definitely isn't, using today's commodity data storage tech.