I wonder what in the world could be cause for such legal arguments??
This is fairly routine in point of fact. Many matters require a ruling from the judge, but these discussions (arguments is the legal term, but it does not necessarily mean it is disputatious) always take place in the absence of the jury. In a judge alone trial, or in an appeals court proceeding, you don't tend to notice them so much because there is no jury involved.
It is also routine during a jury trial not to report on matters discussed in court in the absence of the jury. This makes it far less necessary to "sequester" the jury - keep them in isolation in a hotel for the duration of the trial, an extremely onerous, not to mention expensive, procedure.
It doesn't mean that people in court can't share what they heard with their family over dinner (provided they have no connection to the case), it just means it can't be published until the trial is concluded.
Matters include quite minor questions of procedure, questions concerning admissibility of particular evidence, presentation of qualifications of a potential witness to be declared an "expert witness" (shades of the Dr. Charles Smith fiasco -- he should
never have been considered an expert witness on forensic pathology, in which he had no qualifications whatever, and protocols for qualifying a witness to be an expert in a field have since been made more specific and subject to approval).
It can also be something major, too, of course, such as an accused changing his or her plea, or challenging evidence to be introduced that was not (purportedly) disclosed.
Sometimes the judge takes these matters under advisement because he or she wishes to consult legal precedent or related cases before making a decision.
