I actually filed this seam issue a while ago at http://dev.processing.org/bugs/show_bug.cgi?id=602 and it's something that you need to hack around for the moment, until the internal fixes get put into Processing.

BTW, though that bug is currently marked as a dupe, I'm not so sure I agree - if the fix to the other bug takes care of this I will happily recant, but I couldn't figure out the connection between the two.  I did finally alter my version of Processing's OpenGL library to fix this issue, but I have to dig through it and see exactly what I did because it's been a while.  I know it was essentially what I mentioned in that bug report, and it worked with some changes, but I have to track them down and make sure it's all properly working for any weird edge cases.  Anyhow, once I get it all sorted out I'll submit a fix for one of the next releases.

The workaround, at least if you're using textureMode(NORMALIZED), is that before every

vertex(x,y,z,u,v);

call that you make you map the texture coordinates slightly away from the edges like so:

u = map(u,0,1,0.01,0.99);
v = map(v,0,1,0.01,0.99);

(this is something like the middle of pixel thing discussed before, though not exactly)

This is not ideal, because it slightly zooms the texture, but it works for the most part (you can play with the .01 and .99 to tune exactly how far away from the edge you map the textures).