Do the "watchman" passages apply to all Christians? I have heard it preached—and I myself have preached—that when we fail to take advantage of an opportunity to share Christ, the blood and guilt of the person we failed to evangelize is on our heads. Is this thinking biblical? 

Excellent question—thanks. Ezekiel 3:16-21 and also 33:1-20 feature commands to the prophet Ezekiel to deliver God's message of judgment. Obviously we aren't all "prophets"—yet we are all given the Great Commission (Matt 28:19-20). We have different roles, just as we have different gifts. As Paul notes, "I planted, Apollos watered, but God caused it to grow. So neither the one who plants counts for anything, nor the one who waters, but God who causes the growth" (1 Cor 3:6-7).

As I've recently been studying Ezekiel, I am re-reading a great book I read it back in 1986 (one of those you don't give away). The author is Jim McGuiggan, a fiery yet wise brother from Northern Ireland. Here's an excerpt worth its weight in gold:

[Ezekiel 3:16-21] doesn't teach that God will hold us responsible for failure to teach. He does teach us here that rebellion will result in our destruction. He does teach us that impenitence with regard to failure to teach will cost us all. If we were to be held for every responsibility to teach a soul, who would be saved? Too many people live under the crushing burden of fear that they will be lost because they have failed to take an opportunity presented to them by God to teach some poor soul. This is not Bible! If we don't care about our obligation to to Christ to share our faith then we'll die without him; but this is true about any responsibility God has laid on us.

I tire of hearing preachers make this the crime of crimes while they themselves gallivant all over the nation and the world preaching to the saved and neglecting home responsibilities. If the preachers would get on with the evangelizing rather than spending the bulk of their time trying to get everyone to be evangelists I believe we'd get more evangelizing done.

I'm trying to urge evangelists to evangelize. I'm not trying to discourage the spread of the word by all of the members all of the time to all of the world in all possible ways—I'm asking evangelists to recognize their peculiar calling... Let these whip-cracking preachers get on with the job of spreading the word instead of trying to build a vibrant church on the sweat, blood and guilt of the people who work to pay their salaries. We've had enough pyramids and enough pharaohs—let's leave them in the dust where they belong.

From Jim McGuiggan, The Book of Ezekiel (Fort Worth, TX: Star Bible Publications, 1979), 42-43

Elder Ron Sawhill (Athens, Georgia) weighs in:

The watchmen protected the city. They weren't primarily an offensive team, but a protective, defensive team. While we are all called to be responsible for one another (Heb 3:12-13), the role of the watchman wouldn't seem to be to apply to non-believers, but rather to make sure believers are doing well. The evangelist's role is different. Yes, we are all responsible to proclaim the message, but it is a lot easier to follow someone who is out in front doing it and calling others to follow than someone who spends all his efforts pushing from behind. Guilt is not the right motivator and would not be in the class of "building with gold, silver and precious stones" (1 Cor 3:12), but I would think definitely falls into the combustible wood, hay and straw category.