As with Cordova 3.5 (at least), objects FileReaderonly accept objects File, not objects FileEntry(I'm not sure about previous releases).
, readme.txt . - FileEntry.file(...). File, FileReader.readAs.
function readFile() {
window.requestFileSystem(window.LocalFileSystem.PERSISTENT, 0, function(fileSystem) {
fileSystem.root.getFile('readme.txt',
{create: false, exclusive: false}, function(fileEntry) {
fileEntry.file(function(file) {
var reader = new window.FileReader();
reader.onloadend = function(evt) {console.log(evt.target.result);};
reader.onerror = function(evt) {console.log(evt.target.result);};
reader.readAsText(file);
}, function(e){console.log(e);});
}, function(e){console.log(e);});
}, function(e) {console.log(e);});
}