Funny... I popped in here specifically to see if anyone else was having this issue, and this was on the first page.
It's exactly what you're describing. The speech starts normally, then it suddenly stops for just a second in the middle of a line, and continues immediately afterwards. It seems like it skips several seconds of the speech though, not just the half a second it's cut out for.
I don't remember this happening in older versions, but I only played about 10 hours before 1.4 came out. I'm using SKSE now (for SkyUI), so I'm going to try loading the game without either and see if it's still happening.
^^Tried it without SKSE and SkyUI, no change. Definitely seems far more likely to happen if I'm moving when the dialog is playing... I tested this talking to a guard in Whiterun. If I hit E and immediately back away, some of the speech gets cut out about 50% of the time. If I stand still it doesn't seem to happen. Nothing has changed about my system since I played with the pre-patch version, and I'm not using any other mods.