Answer choice D is incorrect because "judges are rarely allowed to sit on cases when they are biased" is not something that the author would consider to be an effect of the current approach to recusal and disqualification. Rather, the author states that there are, in fact, cases where bias is overlooked.
Answer choice E is correct because we know that "in some jurisdictions, statutes allow a party to a court proceeding to request disqualification of a judge for bias" (lines 8-10). The author then describes this mechanism as "unreliable" (line 33)
As for whether some cases of judicial bias are undetected, this is supported by lines (22-24). "Focusing on appearances may cause sources of actual bias that are not apparent to outside observers, or even to judges themselves, to be overlooked."