Race Comment Explainer

Original comment with matches highlighted:

towards rear, o dispu 3f out, pushed along to dispute 3rd 2f out, ridden and final

Matched phrases & meanings

Phrase	Meaning
Pushed along	The jockey started to urge the horse (hand-riding, not necessarily using the whip).
Towards rear	Running near the back of the field.
No extra	Did not improve or accelerate when asked.
Furlong	Unit of distance; one furlong is 1/8 of a mile (approx. 200 meters).
Headway	The horse was moving up through the field.

Summary

The jockey started to urge the horse (hand-riding, not necessarily using the whip).
Running near the back of the field.
Did not improve or accelerate when asked.
Unit of distance; one furlong is 1/8 of a mile (approx. 200 meters).
The horse was moving up through the field.