self.tableView.reloadData() not working in Swift

You’ll need to reload the table on the UI thread via:

//swift 2.3
dispatch_async(dispatch_get_main_queue(), { () -> Void in
    self.tableView.reloadData()
})

//swift 5
DispatchQueue.main.async{
    self.tableView.reloadData()
}

Follow up:
An easier alternative to the connection.start() approach is to instead use NSURLConnection.sendAsynchronousRequest(...)

//NSOperationQueue.mainQueue() is the main thread
NSURLConnection.sendAsynchronousRequest(NSURLRequest(URL: url), queue: NSOperationQueue.mainQueue()) { (response, data, error) -> Void in
    //check error
    var jsonError: NSError?
    let json: AnyObject? = NSJSONSerialization.JSONObjectWithData(data, options: NSJSONReadingOptions.allZeros, error: &jsonError)
    //check jsonError
    self.collectionView?.reloadData()
}

This doesn’t allow you the flexibility of tracking the bytes though, for example you might want to calculate the progress of the download via bytesDownloaded/bytesNeeded