Taking and saving pictures using promises
Promises were meant to provide a linear appearance of async code instead of callbacks, as well as make it appear that the control is in one place rather than handing it off to other functions.

Also, functional programming is also of help. Not to the strict sense though, but trying to avoid side effects as much as possible as well as isolating code that mutates stuff to a few known locations can help you reason about your code.

// Let's just move out the handler so both getPictures and takePictures
// look the same.
$scope.takePictures = function () {
  document.addEventListener("deviceready", _takePictures, false);
}

$scope.getPictures = function () {
  // Taking this as an example, we call an async operation
  getImagesFromDevice({
    quality: 50,
    destinationType: Camera.DestinationType.DATA_URL,
    sourceType: Camera.PictureSourceType.PHOTOLIBRARY,
    targetWidth: 200,
    targetHeight: 200
  }).then(function(imageData){
    // When the operation succeeds, this function is called. The nice thing
    // about promises is that if you return a promise, the next chained
    // then listens to that promise instead of the original.
    return saveFileToParse(imageData);
  }).then(function(response){
    // What the above means is that this function now listens to
    // saveFileToParse instead of getImagesFromDevice
    //
    // Also notice that we isolate mutation to the scope to only here
    // and removed it from the other functions.
    $scope.activeExercise.images.push(response._url);
    $scope.$apply();
    $scope.customImage = true;
  });

  // In the end, your operation looks linear
}

function _takePictures() (
  getImagesFromDevice({
    quality: 75,
    destinationType: Camera.DestinationType.DATA_URL,
    sourceType: Camera.PictureSourceType.CAMERA,
    allowEdit: true,
    encodingType: Camera.EncodingType.JPEG,
    targetWidth: 200,
    targetHeight: 200,
    popoverOptions: CameraPopoverOptions,
    saveToPhotoAlbum: true
  }).then(function(imageData){
    return saveFileToParse(imageData);
  }).then(function(response){
    $scope.activeExercise.images.push(response._url);
    $scope.$apply();
    $scope.customImage = true;
  });
}

// These operations do not concern what you're doing with the data. All
// they know is that they receive options, operate, and hand you back
// the data when done. Pretty functional don't you agree?

// Another perk about promises is when you don't return a promise in the
// sequence, all chained thens will resolve using the same value. This
// allows us to chain a then for logging in between without affecting
// the result.

var getImagesFromDevice = function (options) {
  return $cordovaCamera.getPicture(options).then(function (imageData) {
    // logger for success
  }, function (err) {
    // logger for error
  });
}

var saveFileToParse = function (imageData) {
  return (new Parse.File("mypic.jpg", {
    base64: imageData
  })).save().then(function (response) {
    // logger for success
  }, function (error) {
    // logger for error
  });
}


Now if I were to write all this code synchronously, which is how a normal person would go about imperative programming (commands one after the other), the code appears 95% the same.

$scope.takePictures = function () {
  document.addEventListener("deviceready", _takePictures, false);
}

$scope.getPictures = function () {
  var imageData = getImagesFromDevice({
    quality: 50,
    destinationType: Camera.DestinationType.DATA_URL,
    sourceType: Camera.PictureSourceType.PHOTOLIBRARY,
    targetWidth: 200,
    targetHeight: 200
  });

  var response = saveFileToParse(imageData);

  $scope.activeExercise.images.push(response._url);
  $scope.$apply();
  $scope.customImage = true;

}

function _takePictures() (
  var imageData = getImagesFromDevice({
    quality: 75,
    destinationType: Camera.DestinationType.DATA_URL,
    sourceType: Camera.PictureSourceType.CAMERA,
    allowEdit: true,
    encodingType: Camera.EncodingType.JPEG,
    targetWidth: 200,
    targetHeight: 200,
    popoverOptions: CameraPopoverOptions,
    saveToPhotoAlbum: true
  });

  var response = saveFileToParse(imageData);

  $scope.activeExercise.images.push(response._url);
  $scope.$apply();
  $scope.customImage = true;

}

var getImagesFromDevice = function (options) {
  var imageData $cordovaCamera.getPicture(options);
  imageData ? /* success logger */ : /* error logger */;
  return imageData;
}

var saveFileToParse = function (imageData) {
  var response = (new Parse.File("mypic.jpg", { base64: imageData })).save();
  response ? /* success logger */ : /* error logger */;
  return response;
}


Now I'm assuming here that you use a "standard" promise. Angular's $q has a weird quirk where if you don't return anything from the resolve or reject handler, instead of resolving or rejecting with the same value from the original promise, it resolves regardless.

The fix is to manually return data or a reject.

var getImagesFromDevice = function (options) {
  return $cordovaCamera.getPicture(options).then(function (imageData) {
    // logger for success
    return imageData;
  }, function (err) {
    // logger for error
    return $q.reject(err);
  });
}