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'British Royal Navy forces against the forces of the Kingdom of Holland,' - Repetition of 'forces'
Repetition of 'was able' in the second paragraph of the lede
'At the start of 1806, control in the Indian Ocean in the Napoleonic Wars was disputed' - 'of the Indian Ocean' would seem better.
'but were still insufficient' - 'but their forces were still insufficient' needs to be added, I think, as we're referring to the British being unable to effect complete control of the ocean. Either that or replace 'insufficient' with 'unable'. Either/or, really.
Repetition of 'too concerned' in Background section
'Batavia roads' - What context is 'roads' used here? It doesn't seem to have been used previously.
'Captain Pellew opened fire on the other grounded ships while boats boarded them in turn' - Should probably be clarified, as I doubt he fired when the boats were actually boarding the vessels!
Couple of instances in the Griesse section where you use variations on 'without a single casualty', and it seems a little peacockish; I'd suggest getting rid of 'single' to make it more neutral.