Having never seen a little ringed plover I confess to knowing little about them and so looking at the results of your tweets has been quite an education. In my early years 'birding' before I diversified into other interests little ringed plover were considered rare but that was in Hampshire so whether they have always been frequent visitors to Dorset or whether it is just that they are increasing un numbers I do not know. They nest in man-made habitats like quarries and gravel pits and there are a number of those here in Dorset however I do not think many, if any now, have breeding pairs. We must assume, I think, that the birds seen in Dorset are migratory passage migrants.
The weekly report charts is interesting. It seems that little ringed plover start passing through the county in late March from week 10 onwards, there is certainly a rush of records from week 12 to 17 during April. Numbers seem to reduce in May before an upturn in June and July, particularly weeks 24 to 31. There are the occasional reports through until week 35 in September and then nothing until the following spring. The RSPB Handbook of British bird says they are early breeders starting in April and that by June or July they have left their breeding territories and have dispersed; that seems to tie in with the reports from here in Dorset.
The vast majority of reports come from Lytchett Bay and records in general come from coastal sites, especially where there is sheltered tidal mudflat habitat such as the Fleet, the western end of Poole Harbour and in Christchurch Harbour.
Having never seen one myself I am hardly the person to tell you how you might get little ringed plover on to your Dorst list!