What are the disadvantages of non-standard analysis? Most students are first taught standard analysis, and the might learn about NSA later on. However, what has kept NSA from becoming the standard? At least from what I've been told, it is much more intuitive than the standard. So why has it not been adopted as the mainstream analysis, especially for lower-level students?

NSA is an interesting intellectual game in its own right, but it is not helping the student to a better understanding of multivariate analysis: volume elements, $ds$ versus $dx$, etcetera. The difficulties there reside largely in the geometric intuition, and not in the $\epsilon/\delta$-procedures reformulated in terms of NSA.
We are still awaiting a "new analysis" reconciling the handling of calculus using the notation of engineers (and mathematicians as well, when they are alone) with the sound concepts of "modern analysis".
And while I'm at it: Why should we introduce more orders of infinity than there are atoms in the universe in order to better understand $\int_\gamma \nabla f\cdot dx=f\bigl(\gamma(b)\bigr)-f\bigl(\gamma(a)\bigr)\>$?
