If I am traveling across time zones, such that I lose time, does that pose a problem for counting the Omer, since the traveling day is not "complete" (it is less than 24 hours)? (I suppose two days could be less than 24 hours if nightfall occurred while in the air.) If you say that the time is made up when I return (when I would have a day or two that is longer than 24 hours), such that I would have counted 49 complete days by the end of the omer period, then what if I am not returning until after Shavuot? Then I would definitely not be counting 49 complete days. Is that a problem?

ב"ה Shalom The Rabbis discussed this issue and decided, that even if a person has a shorter day during the Omer due to travel, this does not pose a problem as far as the "Temimot"= complete days issue is concerned.This how Rav Mordechai Eliyahu zt"l ruled (צידה לדרך pg. 140) and so did many others.)(See ( פסקי תשובות סי' תפט:( The bigger problem is if one loses or gains an entire day, which is also discussed in the aforementioned books. All the best Shabbat Shalom and Chag Same'ach.