Freedom of Speech -- do you still have this right in the military?

I would say your freedom of speech is limited, and yes they should be punished for bad mouthing leadership on social media. You are a Soldier 24 hrs a day and UCMJ applies at all times.

People have the freedom of speech. Government only has the authority delegated to them by the people by the constitution.

A service member is not a person, he is a government agency. We do not have the right to speak our minds while acting as a representative of the government.

Also, don't leaders have better things to do than spy on their subordinates' social lives?

When we take our enlistment oath, we don't give up our freedom of speech...it just may not be heard. In a sense, we elect to have leadership speak and make choices for us the moment we say, "so help me GOD".

yes you do... sunject to restrictions of the UCMJ. the military is NOT a democracy

Oh you can say there is freedom of speech in the military,... but in reality.... I do not believe there ever was freedom of speech in the military... without having the fear of retaliation by a court-martial or being drummed out of the service or being put on the worst details you can imagine....
Should a soldier put something on social media you ask...... only if he wants to go to the brig..... so no I would say that is definitely unwise.... for the most part you keep your head down and your mouth shut..... otherwise you would be hearing about a lot of missions that happened to get the benefits that the veterans so rightly deserve.... but cannot speak up because it is still classified, or the government doesn't want to pay out on the claims.... and you are branded a liar or branded for treason....

freedoms come with responsibillities and accountabillity, think first act second

Well, here is where I have to disagree with you 1SG. You can have all of the oratory freedom you want, as long as your rank can afford it. See, in today's Army (at least, the Army, I cannot speak for other branches), and especially in TRADOC, if you are below the rank of E-6 (SSG), then you do NOT have the freedom to say or do ANYTHING that draws attention to you, unless you want to have your fourth point of contact in a sling. Believe me, the IET Privates have more freedom than you do as Support Cadre (Non-Command or DS). I cannot speak freeliy, or offer an opinion at any given time, except on here, or on Facebook. and I've gotten a royal a** chewing more than once for speaking up on both of those outlets as well, because it is "counterproductive to unit cohesion and it hints at insubordination."

Not true, at least in the af. I had to advise people of their rights when questioning them. We had to get the equivalent of a search warrant before we could search dorm rooms or anything like that. Vehicle searches at the gates were warrantless but bug signs warned anyone coming on base that they were possible. Also, even those were restricted and carefully monitored. I saw little difference in civilian law enforcement practices and the way we did things in Air Force Security Police.

I think by posting on social media, while in active duty, (or is it 'on' active duty?) Should probably be abstained. Too much bad things can be done and unintentionally as well...too much room for error...

I think people forget that with freedom of speech come responsibility.

And, there is no guarantee that there will not be consequences for what you say.