We encountered some problems with ATMs, but could not establish the cause. It never became a real obstacle, but I think it is useful to take some cash with you as well. Dollars are accepted everywhere. Western Union appears to have offices in even the remotest villages.
I do not want to say something unkind about the people of Syria, Jordan, or Egypt, but there is no denying that over there, western women attract a lot of unpleasant attention. Nothing of that kind will happen in Lebanon, although a scarf is required in a mosque.
To sum up: travel is not always easy in Lebanon, but it has a great potential for tourism, and there is very much to be seen. However, the most important thing we learned is that the Lebanese are, easily, the friendliest people in the Near East. I have already decided to return next year, with a group, and can recommend a visit to everyone.
(If you understand Dutch, you can read my travel notes here.)