Plant cells have rigid cell walls to hold the cells together, how do animal cells hold themselves together. Does it have something to do with the chemical properties (dipoles) of the phospholipid bilayer?

Well animal cells are obviously not nearly as rigid as plant cells, compare a hunk of meat to a tree branch. Animal cells do have a large number of structural proteins, and especially the cytoskeleton, that allow them to form into specific (though elastic) morphologies.

Animals have either bones or exoskelitons to hold them together, plus they need a more flexible cell membrane in order to move

The phospholipid bilayer of animal cells is very fluid on its own. It is reinforced by 'plates' of cholesterol which buffer the motion of the phospholipid molecules, which are spinning like ballerinas, and occasionally will even flip from one layer to the other. Without these cholesterol plates, the cell membrane would have little more integrity than the meniscus layer of water.

 

As Skye said, cell integrity is further helped by the cytoskeleton, and also the proximity of other cells and support tissues. The whole lot is helped further by the intra and intercellular pressure being slightly less than one atmosphere, so air pressure helps maintain tissue tone also.

spindle fibers help (they are part of the cytoskeleton) and the lipid bilayer, just to let you know, is bipolar, which means that one end is hydrophilic, and theother is hydrophobic, keeping the cell wall from falling apart. just in case you wanted to know.