value of select elements with “e.value” vs “e.options[e.selectedIndex].value”

Answer 1

Some old (~2005) threads from the comp.lang.javascript newsgroup, as well as their FAQ [1], mention that .value access was not supported in Netscape Navigator 4 (i.e. pre-2000), and some other mobile and desktop browsers that were considered "old" even at that time.

Conclusion (backed by @Oriol's DOM spec excerpts): It's totally safe to use today.