Lateen sails took a particularly long time to spread. They had been introduced to the Mediterranean region as early as the 2nd century BC (and had been developed much earlier in China and Arabia), but were not brought into widespread use in European sailing ships until the 1400s. This is
hugely significant as a lateen-rigged ship can sail far closer to the wind than a square-rigged ship, giving it much better maneuverability, allowing it to navigate complex waters (e.g., harbour entrances) under less-than-ideal conditions, and increased the length of the sailing season -- November through May was "no-sail" season from Roman times (with numerous interesting impacts on historical events, messages, etc.).
The rig seems to be among the technologies lost during the middle ages.
The big hitch, as noted in James Burke's Connections, was how ships and sailing voyages were financed. A ship was a sufficiently sizeable investment, and financing sufficiently difficult to arrange, that conservative financiers opposed any radical explorations of such tomfoolery as them thar lateen-rigged newfangled boats.
As for other transportation innovations ... there mostly weren't any until quite modern times.
Once introduced, though, their advantages were immediately obvious, and they were adopted quickly throughout Europe.
https://en.m.wikipedia.org/wiki/Lateen
Yes, you saw further advances in ships and navigation. Especially navigation -- position-taking and timekeeping were critical, and several innovations followed catastrophic losses of entire fleets run aground and shipwrecked into the 20th century -- see the Honda Point disaster in which seven US destroyers sailed at full speed into rocks just offshore the Santa Barbara coast in 1923.
https://en.m.wikipedia.org/wiki/Honda_Point_disaster
After the Lateen rig and excepting other ship designs, the major transport innovations were canals (major construction from the 1500s onward in Europe, though much earlier in China, and some earlier European/Mediterranean instances), the railroad (1825), steamship (1810s), safety bicycle (1870s), automobile (and truck and bus -- 1880s), and airplane (1900s). These all spread essentially instantly throughout the world wherever industrial capacity (and fuel) capable of producing such vehicles existed.