I would support Unwashed's suggestion about mowing, if there is not much grass on the rough patch, you could always chuck down some cheap seed. If you fill in the worst holes from the biggest hummocks before sowing, you might even get a mower over it which is quicker than using a strimmer. The turf will out-compete the weeds if mown and improve the soil when dug over in the autumn.
Alternatively if you decide to go down the spot weeding route I have had good experiences using widely spaced sweet corn as a cleaning crop.