Smoothing seams on Textures

There are a few tutorials on this already, here is my take on the subject. Some textures have inherent seams and so they do not cause a joining problem. The classic beach ball is an example. Some textures are meant to be smooth and continuous. Lets start with an example of what we do not want to do:

Applying this test texture may make the problem clearer, in the process of applying the texture to the object the texture is wrapped all the way round so the left and right edges join up. Actually on the innertube the top and bottom edges join in the "hole", but as its on the inside its not so obvious, and a visible seam is more forgivable.

In this next example the fill starts and ends on the same colour so the join will be smooth and will not leave a visible seam.

Another method is to paint over the seam. To illustrate this I'll start with a semi-random "blobs" texture generated by Photoplus.  The edges of the texture do not join up so inevitably there is a seam. It is possible to generate repeating textures but they tend to look geometric.

First using simple copy and paste we swap the left and right hand halves of the image, putting the seam in the middle. This does not improve the texture, but it makes the seam visible in our editor.

Version with the seam visible as described above

Then we just paint over the seam to smooth it out. This may be accomplished using a "clone" brush, but for this texture a simple slightly softened paint brush is sufficient.