The Modifier in the second part of this sentence -- describing what dieters will blame for the failure of a diet plan -- explains why dieters may prefer a potentially ineffective plan to an effective one. Therefore, the sentence must be structured in a way that correctly indicates this Meaning. Additionally, there should be proper Parallelism between the two possible explanations given for the failure of the plan (i.e., the plan's ineffectiveness versus the dieters' lack of self-control).
(A) CORRECT. A diet plan whose effectiveness is uncertain clearly and unambiguously indicates the nature of the uncertainty described: the effectiveness of the diet plan (not, say, the particulars of the plan itself) is uncertain. The following appositive modifier (a consideration that…) is properly used to describe the entire preceding idea, namely, the idea that the diet plan's effectiveness is uncertain. The modifier in case of failure is set off by a comma from the entire parallel structure, properly indicating that the entire parallel structure (not just one of the parts) describes the situation in which the diet plan fails. Finally, the structure X rather than Y is formed with proper parallelism: both X (the supposed ineffectiveness of the plan) and Y (their own lack of self-control) are noun phrases.
(B) The phrase an uncertain diet plan in terms of effectiveness is unclear: it seems to indicate that the diet plan itself, rather than the plan's effectiveness, is uncertain. There is a lack of agreement between the plural plans (at the start of the second clause) and the singular plan (in the first clause); better agreement would be achieved if such plans were replaced with such a plan. Finally, the modifier in case of failure is attached only to the second option in the parallel structure (that they lack self-control); this modifier should be placed so as to modify that entire parallel structure.
(C) This choice places the two infinitives to blame… and to lack… in parallel, thus creating a nonsense meaning: the (illogical) implication is that the diet plan will allow them to blame and [will allow them] to lack self-control. This is incorrect; the dieters' second option is to blame a lack of self-control.
(D) The phrase uncertainly effective diet plans is unclear. The comma + allowing... modifier should refer to the action of the preceding clause (many dieters subconsciously prefer…), but this meaning is nonsensical; it is not the case that, because the dieters prefer an uncertainly effective diet plan, this fact allows them to believe that the plan is ineffective. The two factors that could potentially be blamed are not written with proper parallelism: the first is a noun phrase (the plans…), while the second is an entire clause (that they lack self-control). Moreover, the first of these factors is written illogically: to believe the plans erroneously indicates that the dieters believe the plans themselves, when in fact the opposite is true, i.e., the dieters actually don't believe that the plan is effective.
(E) In this choice, the portion following the semicolon (allowing them to believe…) is a modifier, not a complete sentence. A semicolon must be followed by an independent clause (a complete sentence) containing both a subject and a verb.