Can I visualize (show) changeset on a map somehow?

You are not correct, a changeset lists all changes. However it does not have enough information to plot it on a map because if e.g. a way tag is changed, the changeset does not necessarily contain all the way's nodes and thus it lacks information about the node geometry. Visualizing a changeset requires a local database with all OSM data.

There is a tool in SVN that plots the difference between two osm data sets, called osmdiff but I don't know of anything that actually plots a raw changeset.

Depending on what you want to do, you may find these tools handy:

ITO World OSM mapper

OWL: OpenStreetMap Watch List

They both let you look at map changes in an area over a certain period of time.

As the previous answers are 3 years old, as a few services are not available anymore, and as I was looking for a few tools, here is my go at answering your question:

The closest I found to what you are/were looking for is the experimental OWL history tab that lets you have a look at the history of changesets in a zone, with clickable elements and tree-like view of changesets.

Hopefully there will soon be new fancy useful tools, or others will resuscitate somehow.

it would be useful to have JOSM highlight additions and modifications (deletions are obviously more difficult) based on a OSM change file. or you can generate a find/filter string from a OSC file using XSLT.