The critical thinking skills associated with recognition and handling of vagueness and ambiguity would certainly have a bearing on language skills generally, including those involved in second language acquisition. Many native speakers make poor informants about their own language, tending to overgeneralize from their idiolect, which may harbor ambiguities and vaguenesses of which they are unaware.
I used critical thinking to teach vocabulary in L2- English
for example I would ask them do you know the word assimilation? They would then link to the borrowed word in Malay Which is assimilation. Then I showed them in English how the same word could be a verb etc . Asked them in Malay how this was done. They had to make the links and connections between L1 and L2
If we think about evaluating as a critical thinking skill, while learning an L2, when a learner is asked to read a particular text in the target language and draw conclusions/judgements/opinions on the issue discussed in the reading text, the learner is compelled to make associations between the learner's prior learning/experiences with the newly introduced topic. Doing so, the learner not only has to come up with appropriate expressions related to the issue raised/discussed in the text, but also has to navigate through short and/or long term memory to match prior learning/experience. Does it affect L2 learning negatively or positively? Well, I could think about the positive way such critical thinking stimulates learning for an L2 learner. As Prof. Pfeifer has mentioned in the earlier answer, the native speaking learner may overgeneralize from their idiolectal experiences of learning, but the L2 learner may add a creative dimension in the process through individual input which may sometimes appear as non-conventional output or performance in the learning process.
Critical thinking skills may be developed in several ways at different levels of learning. The three main aspects of critical thinking: finding patterns and relationships, evaluating ideas and using such skills to solve problems differ depending on the learning level.
I've taught both high school and university students. For example, I assigned students exercises in which they were required to identify the main structure of an argument, compare points and arguments from different sources, identify evidence and its reliability, examine possible solutions to a particular problem and say how effective they are, and so on. For another example, I assigned exercises to university students in which they had to compare and contrast different points of view on a given issue, recognize basic weaknesses in argumentation, arrive at nuanced evaluations of ideas and arguments, and identify areas in which to improve an implemented solution.
Critical thinking impacts and is interrelated with a wide range of other skills, including communication and language skills. According to my observations, learners, for example, who are hesitant to express themselves in their native language may be more likely to do so in a second language. Critical thinking helps in improving ESL writing skill, language proficiency, and oral communication ability.
In contrast, many variables 'negatively' influence second language learning, including age, the gap between L1 and L2 (causing interference), cultural factors, and so on.
To add to what Dr. Lahlou has discussed, in order to benefit from critical thinking in language learning and communication, many learners need scaffolded learning tasks which is, as Dr. Lahlou has pointed out, mainly due to the variability of learner proficiency levels occurring due to age differences or, to add, many other factors such as motivations for learning, fossilizations of certain learning habits/errors/previously learnt contents etc.