You shouldn't encounter any particular problems - Lebanon ended conscription a few years ago. The conscription issue used to be a bit of a problem for Lebanese citizens raised abroad who then visited the country, as still happens in Syria and Greece.
There's quite a few checkpoints about, but I've never been IDed at any, despite having visited Lebanon a couple of times for about three weeks each visit. I'd carry a photocopy of passport with you at all times though, just in case.
As for safety, if you do a forum search, you'll find tons of prior discussions on it. In a nutshell, Lebanon is very safe by international standards on a day-to-day basis, with the caveat being that the security situation can profoundly deteriorate extremely quickly - July 2006 and May 2008 came almost out of nowhere. On a day-to-day basis however, crime is very low and people are very friendly and helpful, though the traffic is absolutely batshit crazy - the roads are usually the most dangerous thing in Lebanon.
Tensions are somewhat higher than usual in Lebanon at the moment due to the Hariri Tribunal and the growing threat of conflict between Iran and Israel. Lots of people are expecting some sort of war in the next year (though I wouldn't expect anything to happen over Christmas/New Year) so I probably wouldn't go any further south than Sidon at the moment.
If you're up for partying, then there's plenty of fantastic bars and clubs in Gemmayzeh, Achrafieh and Hamra. You don't need to search too hard. I'd also recommend a night at Music Hall, which is always a hoot, especially at the weekends.
Outside of Beirut, Byblos, Baalbek and the Qadisha would be my absolute must-sees. But there's tons to see and do there, and it's a small country, so just read up and see what you like the look of - you can day trip anywhere from Beirut quite easily.
Enjoy your trip!
