jerky motion using CMMotionManager iPhone

Question 1

A couple of reactions:

I might suggest using gravity rather than attitude, as it nicely represents the physical orientation of the device.
Rather than using a string to hold the value, I might just update the numeric values.
Rather than all of those if statements, just have a formula that represents how the view should be placed.
If you want to move a bunch of views, you should put them in a UIView (commonly called a "container view", not to be confused with the custom container control in IB of the same name) and then just move the container view.

So, if using autolayout, I might have the following properties:

@property (nonatomic, strong) CMMotionManager *motionManager;
@property CGFloat top;
@property CGFloat left;

And then I can update the autolayout constraints like so:

self.motionManager = [[CMMotionManager alloc] init];
self.motionManager.deviceMotionUpdateInterval = 0.05f;

self.top = self.topConstraint.constant;
self.left = self.leadingConstraint.constant;

[self.motionManager startDeviceMotionUpdatesToQueue:[NSOperationQueue mainQueue] withHandler:^(CMDeviceMotion *motion, NSError *error) {
    self.leadingConstraint.constant = self.left - motion.gravity.x / 8.0 * 100.0;
    self.topConstraint.constant     = self.top  - motion.gravity.y / 8.0 * 100.0;
}];

Or if not using autolayout:

@property (nonatomic, strong) CMMotionManager *motionManager;
@property CGPoint originalCenter;

and

self.motionManager = [[CMMotionManager alloc] init];
self.motionManager.deviceMotionUpdateInterval = 0.05f;

self.originalCenter = self.containerView.center;

[self.motionManager startDeviceMotionUpdatesToQueue:[NSOperationQueue mainQueue] withHandler:^(CMDeviceMotion *motion, NSError *error) {
    self.containerView.center = CGPointMake(self.originalCenter.x - motion.gravity.x / 8.0 * 100.0, self.originalCenter.y - motion.gravity.y / 8.0 * 100.0);
}];

Frankly, having the motion manager operate in the main queue gives me the willies, so I might (a) create a NSOperationQueue for the motion updates and only update some class property; and (b) use a CADisplayLink (part of the QuartzCore.framework) to update the view (if needed). Thus:

@property (nonatomic, strong) CMMotionManager *motionManager;
@property (nonatomic, strong) NSOperationQueue *motionQueue;

@property (nonatomic) CMAcceleration gravity;
@property (nonatomic) CGPoint originalCenter;
@property (nonatomic) BOOL updatePosition;

@property (nonatomic, strong) NSMutableArray *angles;
@property (nonatomic, strong) CADisplayLink *displayLink;

and

- (void)viewDidDisappear:(BOOL)animated
{
    [self stopDisplayLink];
    [self.motionManager stopDeviceMotionUpdates];
    self.motionManager = nil;
    self.motionQueue = nil;
}

- (void)viewDidAppear:(BOOL)animated
{
    [super viewDidAppear:animated];    

    self.motionManager = [[CMMotionManager alloc] init];
    self.motionManager.deviceMotionUpdateInterval = 0.05f;

    self.motionQueue = [[NSOperationQueue alloc] init];
    self.motionQueue.name = [[[NSBundle mainBundle] bundleIdentifier] stringByAppendingString:@".motion"];

    self.originalCenter = self.containerView.center;
    self.updatePosition = NO;

    [self.motionManager startDeviceMotionUpdatesToQueue:self.motionQueue withHandler:^(CMDeviceMotion *motion, NSError *error) {
        @synchronized(self) {
            self.gravity = motion.gravity;
            self.updatePosition = YES;
        }
    }];

    [self startDisplayLink];
}

- (void)startDisplayLink
{
    self.displayLink = [CADisplayLink displayLinkWithTarget:self selector:@selector(handleDisplayLink:)];
    [self.displayLink addToRunLoop:[NSRunLoop currentRunLoop] forMode:NSDefaultRunLoopMode];
}

- (void)stopDisplayLink
{
    [self.displayLink invalidate];
    self.displayLink = nil;
}

- (void)handleDisplayLink:(CADisplayLink *)displayLink
{
    @synchronized(self) {
        if (!self.updatePosition)
            return;

        self.containerView.center = CGPointMake(self.originalCenter.x - self.gravity.x / 8.0 * 100.0, self.originalCenter.y - self.gravity.y / 8.0 * 100.0);

        self.updatePosition = NO;
    }
}

Question 2

I did the following: A math that takes the max and minimum values within a adjustable window (flicker noise) and takes the average. No more oscillations!!!

Here is my code to avoid flickering in may app:

float xAxis,yAxis, zAxis;
xAxis = self.manager.accelerometerData.acceleration.x;
yAxis = self.manager.accelerometerData.acceleration.y;
zAxis = self.manager.accelerometerData.acceleration.z;

// returns if the phone is lying on the table:
if (zAxis < -0.8 || zAxis > 0.8) return;

CGFloat angle =  atan2f(xAxis, yAxis ); // The angle!!!

float noise = 0.011; // Flicker noise (the noise you want to filter)

// max and min are global variables
if (angle > max){
    max = angle;
    min = max - noise;
}
if (angle < min){
    min = angle;
    max = min + noise;
}

// Average: (no flickering):
angle = min + (max - min) / 2.0;