Uneven Speed

Yes - what you described is typical of not enough voltage getting to all parts of the track/layout.  Ways to check include using a meter (typically a DVM) to take voltage measurements all around the track - you could also use a lighted piece of rolling stock and see if the lights dim at different points around the track.

If you only have one connection to the track from your transformer, the voltage starts to decrease as it gets further and further away from the connection point due to voltage losses from things like the resistance in the track so, by the time you get 180 degrees away from the one connection point, the voltage is low enough to affect the speed of the engine.

The solution is to add multiple "power drops"  around the layout about every 4-6 feet, i.e., connect your transformer leads to the track at different locations, instead of just one power connection to the track from the transformer. There are various ways to do this, but one easy way I like is to run your transformer power to a distribution/terminal block like the one below and then run twisted pairs of wires from the ports to as many different track locations as you think you may need, based upon the size and layout of your track.

You can also run "bus" wires around the track underneath the layout and connect to the track with "suitcase" or other connectors.

@Tom Lake posted:

I have a couple Lionel sets, one old (1950s) O gauge track oval that was my Dad's and one brand new Fastrack oval. On both ovals, the train is very much faster near the transformer section than at the other end of the oval. It seems like this is probably normal for electric trains but is there a way to even it out so I get a more constant speed all the way around the track?

I second the above, MORE POWER DROPS every 4-6 feet of track.