The Historic District

I'd have expected oakum to be behind that caulk, between the frame and brick wall, possibly white oakum (just fibres stuffed in there). The black stuff could have been used to prevent the oakum from getting wet in driving rain. Pointing wouldn't seal the seam completely as the wood expands and contracts. I'm not sure I'd use a sealant there - it should be on the inside rather than outside, pointing on the outside and sealing on the inside might be a better idea. If there's nothing behind the caulk (only a gap all the way to the inside) I'd add oakum or maybe expanding foam first and then point on the outside.

The idea is that in a cold climate inside air is more humid than outside air (in terms of absolute humidity) and you don't want warm, humid inside air to get anywhere near cold brick walls or other surfaces where it condenses and potentially rots window frames etc.

If the gap is large I might be inclined (as mentioned) to use a backer rod and a good sealant in the gap, (this is a favorite of mine http://us.henry.com/roofing/roofing-sea ... or-sealant), but then add a quarter round over the top of it, set into the sealant and nailed in place while it is still wet.

for a big gap you could probably use a strip of fir that slips in easy and coat that with your choice of sealant ? it just divides the gap up so it isn't like 1/4" of goo even if you just bury it in there. even paint stir sticks, might not be rot resistant but if you coat them in roof patch or whatever, it probably won't be an issue. if you have a saw you can cut a tapered stick. if you drive it in a bit ( without going crazy) it might bow the jamb a little and change the door clearance slightly and you may or may not want to change the gap. often they use a pair of wedges behind the jamb to set the gap. a pretty similar product to roof patch is "car undercoat" Sometimes I find part cans at garage sales close to free and use it up. I dont; know what the difference is really.. but it's black and goo-ey too
sometimes it's possible to captivat the spray foam and it can move the jamb a little. You can check with different thicknesses of paper or card, just close them in the door and see if they are tight or not to measure the gap. you want some clearance for expansion obviously.