These answers are based on my personal understanding of Bert from both the paper and official_implementation, hope it will help:

    What do they mean by "maximum scoring span is used as the prediction"?
As you know in SQuAD the input sequence is divided to 2 parts: Question and Document (from which we extract the answer if possible). 

Sometimes the input length exceeds the `max_seq_length` parameter, in this case the document is truncated to as many parts as needed and we end up having more than one input for the same question/document. Mention that the question is replicated in all the resulting inputs (see [line_350][1] for details). 

So in such cases, in order to determine the **predicted span** among all the generated-inputs we use the **maximum scoring** *i.e* `(max_start + max_end) / 2 = ( max(Softmax(S*Ti)) + max(Softmax(E*Ti)) ) / 2` of all the inputs related to the same question.

    "The training objective is the loglikelihood of the correct start and end positions"
The loss is the average of the start_position_loss `start_loss` and the end_postition_loss `end_loss`. Each loss is computed in the same way: after applying the Softmax to the final output (i.e `S*Ti` or `E*Ti`) we use the real start/end postitions to compute the loss (see code below).

From [run_squad.py][1] in Bert_repo:

     def compute_loss(logits, positions):
            one_hot_positions = tf.one_hot(positions, depth=seq_length, dtype=tf.float32)
            log_probs = tf.nn.log_softmax(logits, axis=-1)
            loss = -tf.reduce_mean(tf.reduce_sum(one_hot_positions * log_probs, axis=-1))
            return loss
    
     start_positions = features["start_positions"]
     end_positions = features["end_positions"]
    
     start_loss = compute_loss(start_logits, start_positions)
     end_loss = compute_loss(end_logits, end_positions)
    
     total_loss = (start_loss + end_loss) / 2.0


  [1]: https://github.com/google-research/bert/blob/master/run_squad.py