When doing an implicit plot recently, I ended up with a whole large triangle which was completely tessellated with much smaller triangles. The checking of other graphs and numerical data of the function in this region, it was very clear that the implicit function should be a well defined line in this region.
Further look at the code for implicitplot() indicated that, after some setup work, it ultimately called exactly the same routine (`plot/iplot2d`()) as plots[contourplot]() with the option "contours=" to do the actual calculations. I then discovered that when I called contourplot() directly with the "contours=" option I got a correct implicit curve consistent with my other data and with no tessellations.
Why the difference? After checking lots of possibilities, I discovered that the difference was that when implicitplot() called `plot/iplot2d`() it didn't set _EnvInContourPlot = true first while contourplot() did. I then discovered that if I set _EnvInContourPlot = true before calling implicitplot() I got the good implicit plot without the tessellation.