I don't know the longest stage - check Gronze.com I am only half way so far.
The embalse (reservoir) is the biggest problem stage for most people (38km I think). This is because the albergue there has been closed for several years and the only other option is a weird 'fishing hotel' that does not especially welcome pilgrims and I have even heard a report of them taking a reservation and then refusing to open the door.
The morning walk is nice but after about 12km it suddenly changes and becomes grim. First there's a stupid path diversion for railway works and then the trail stays off the roads by repeatedly going up and down annoying small hills, a lot of people give up on that and walk on the roads, which is unpleasant and a bit dangerous. If you are scared of heights like me you'll also find crossing the two N630 bridges somewhat of a trial. On weekends people race around the roads on high powered motorbikes, which provides a spectacle to relieve the tedium but is rather intimidating. The day I was there it was stinkingly hot and there is no shade apart from hiding behind road signs. Oh and I hate reservoirs and dams as well, creepy and scary in my book. But no-one said the VDLP was easy!
My solution was to plan ahead by getting from the owner of the bar Majuca in Casar de Caceres the phone number of lovely Cesar the taxi man from Cañaveral. (Sorry I have lost it now). Plan with others to share the taxi. A good location for Cesar to pick you up is the well signposted gate on the N630 of the boat club
Club Nautico Tajomar, just before the closed albergue, which is about 2/3 of the 38km, so still a substantial stage. Before that point it's difficult to find a place where a taxi could stop where you could also describe your location.
You can also shorten the stage by getting a taxi part way from Casar de Caseres, but then you would miss the beautiful walk in the early part of the day, with the famous cheese making sheep and the lovely cuddly Mastiff at the farm.
Hope that helps.