Critics' concerns include lax rules for the admissibility of evidence and inadequate appeal procedures.
The defence weighed in with frequent objections about the admissibility of evidence.
The home secretary's lawyers emphasised the Jordanians have enshrined into their constitution an "express prohibition on the admissibility of evidence obtained as a result of torture".
It was anticipated that if those detainees were to be tried at all, it would be before a military commission where the touchstone for admissibility of evidence was simply relevance and apparent reliability.
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Before Italy's election this May, lawyers for defendants in each of the three cases of alleged bribery of judges, in two of which Mr Berlusconi is involved, challenged the admissibility of evidence obtained by Italian prosecutors from their Swiss counterparts.
Asked who was to blame for the latest delay, Mrs May said Jordan had changed its constitution relating to the admissibility of evidence allegedly obtained by torture but the new provisions had not been legally tested and there was a difference of opinion over its validity.
The defense said its decision in January to waive a hearing on the admissibility of DNA evidence applied only to results known at the time.
Those had seemed to allow the admissibility of physical evidence found as a result of statements made by defendants before they had heard the Miranda warning.
That judgment, the biggest change in the standard for admissibility of scientific evidence in the federal court system for 70 years, was initially used in civil cases.
Other questions were on the recent escalation of violence in Nigeria, when the Chilcot committee will report on the admissibility of intercept evidence, and how the government's loan guarantee scheme will work.
Lawyers representing Associated Newspapers, which also publishes the Mail on Sunday, challenged a ruling on the admissibility of anonymous evidence at London's High Court before Lord Justice Toulson, Mr Justice Sweeney and Mrs Justice Sharp.
Among the concerns: allegations against Anwar were revealed via the widespread publication of affidavits filed in criminal proceedings against a friend of Anwar's, Solaimai Nallakaruppan, before the judge had ruled on the admissibility of the evidence.
The crossbencher, Lady Cox, wants ministers' assessment of the recent escalation of violence in Nigeria, and the former law lord, Lord Lloyd of Berwick, asks when the Chilcot committee's verdict on the admissibility of intercept evidence in court is expected.
Its first stop would be the Justice Committee, where it could get mired in all sorts of procedural issues, including the admissibility of the main evidence against Mrs Arroyo: purported recordings of her telephone conversations, made without her knowledge or consent.
Taylor based part of his challenge on the admissibility of "multiple hearsay" evidence.
New legislation passed by Mr Berlusconi's government in October was used to challenge the admissibility of the prosecution's evidence, but the judges were unmoved.
Simpson's lawyers renewed their attack on DNA evidence, asking for an admissibility hearing on all test results submitted since they abandoned their pretrial challenge of such evidence.
Although the defence challenged the quality of the evidence, no objection was taken to its admissibility.
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Legal systems as similar as that of the U.S. and Great Britain still diverge on questions like evidence admissibility.
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