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On page 254, paragraph 2 of the Nautical Almanac, it specifies that the volume is based on UT1.  UT1 is based on the rotation of the earth...and hence has a second of variable length.  UTC runs on a second of fixed length, which is slightly shorter than the second of UT1.  At intervals, UTC gets ahead of earth time, and a leap second is inserted to bring it back in sync.

Yesterday, UTC was 0.5 seconds ahead of earth time - which introduced a 0.5 second error in your celestial calculations.  Today, UTC is 0.5 seconds behind earth time (UT1).  So you still have an error = 0.5 seconds in your fix...except the error goes in the opposite direction now.  At some point in the future, since the UTC clock runs fast compared to the earth clock, they will cross over each other, and your fixes will gain in accuracy.

I think of leap seconds not as a way of throwing my almanac out, but rather of modifying the clocks of the world to keep them roughly synchronized with my almanac.