It's worth noting that the only two other bug reports showing up for a search for root.tick.level.connection are MC-11571, which is about a one-time issue on block breaking rather than a continuous lag problem, and MC-12799, which does not provide enough information to conclude whether or not it is the same issue as this or not. I rather think that it isn't, because this particular bug occurs only along a fairly narrow "corridor" of sorts, rather than in a larger general region as MC-12799 describes.
Fixed for me, ATI Mobility Radeon HD 4670 on 64-bit Linux.
Wouldn't the better fix be to pipe all isDown queries through a decoder method that handles -100, etc as the correct mouse buttons? This would also mean future input methods could be more easily integrated with legacy code. This isn't a frequently-called method (relatively speaking) so it would add very little overhead.
It's worth noting that the artefacts observed prior to the texture pack update occurred only on chunk boundaries, whereas these effects now occur on every tile. Based on the fact that it's also adding lines around the edges of transparent textures, I'd hypothesize that the textures are being affected by floating-point rounding issues on getting the texture from the map.
Proposed fix: increase size of drawn textures by half a percent (imperceptible, but sufficient to remove lines). Additionally, decrease size of texture rectangle grabbed from the map by the same amount. Expected performance impact: little to none. Potential issues: Z-fighting between adjacent blocks.
Confirmed on ATI Mobility Radeon HD 4670, Linux Mint 13 (base: Ubuntu 12.10), OpenJDK 7 64bit. Did not occur prior to the texture pack update.
Still present in 1.7.5, 1.7.6-pre2, and 14w11b.