This is an excellent question, and there is some complexity to the answer. First, the interested reader is encouraged to consult our study of the beginning of Acts 19, where Paul properly immersed twelve disciples in Ephesus. They had been baptized previously, but not correctly (cf. 03/23/11 & 03/24/11). Thus, there are certainly situations where one should be immersed again. Second, a series of 3 lessons we posted in 2005 is also helpful for a foundational study of baptism (cf. 03/12/05, 03/19/05, & 03/26/05).
With those thoughts in mind, let's try to answer the question:
(1) Does it matter where one is baptized? The New Testament does not give any indication that it does. Baptism requires enough water for one to be fully immersed, but the location of the water itself is irrelevant (since Jesus never specified, for example, "Go and make disciples, baptizing them in rivers"). That being the case, one could be baptized in a lake, a river, a swimming pool, a bathtub, or even a baptistery--regardless of whether that baptistery is located inside a denominational church building or not. Furthermore, occasionally denominational church buildings that contain baptisteries are sold and purchased by the church of Christ. Is the baptistery now "sanctified" in a special way because the Lord's people now own it? If a baptism was conducted properly in a building while it was still owned by a denomination, would that invalidate the immersion in some way? The answer to both questions is "no." The location of one's baptism is irrelevant.
(2) However, although it doesn't make any difference whether the water for baptism is located in a denominational church building or not, it does make a great deal of difference as to what actually happens in the water. The submitted question deals with a situation that is not common, although it does happen occasionally. It is unusual for one baptized in a denominational church to be immersed for the remission of sins. Typically, such a one is immersed thinking he has already been saved before he ever gets to the water! This is clearly against the New Testament teaching and contradicts the very notion of baptism washing away one's sins and making salvation possible (cf. Acts 2:38; 22:16). If one was not immersed in accordance with what the New Testament teaches regarding baptism, then he should be immersed properly when he learns the truth and seeks to be identified with the church of Christ.
(3) But, the submitted question states that the individual was baptized for the remission of his sins. Thus, based on the provided information, the baptism was (and is) valid. God added that soul to His church when the individual was baptized, even if he immediately departed from God's truth (regarding other aspects of sound doctrine and proper worship) while being joined to a denomination. One who has been immersed into Christ for the remission of his sins is a child of God and a part of God's family (cf. Acts 2:47), no matter how mixed-up he may be on other spiritual matters (e.g., Acts 8:13,19ff).
(4) So, should one who was previously baptized for the remission of his sins in a denomination be baptized again in the Lord's church? I would not require such, since the New Testament does not, but even so, there are cases where it might be a good idea. If the individual has any doubts about whether or not he was actually immersed to have his sins forgiven, then he should be baptized again to remove any doubt. If he has any concerns about whether or not his baptism was valid, then he should be baptized again. If, however, one does not have any doubts about his conversion to Christ and is adamant that he was immersed for the remission of his sins (even if he was mistaken about some other matters while in the denomination), who am I to require him to do something again which he believes he has already properly fulfilled? In that case, I will accept him on his word, knowing that the Lord will, of course, tend to the matter ultimately if something is amiss. In his case, his departure from the denomination is certainly fruit of his repentance. When he seeks to be identified with the Lord's church, it is because he has been taught the way of the Lord more perfectly and wants to leave religious error behind. Making a statement to this affect would be wise, though I would not mandate an explicit public confession. His past religious errors are between he and God. If he has shown the fruit of repentance (by turning from denominational error), and claims to have been immersed in the past for the remission of his sins, and is now seeking to be identified with the church of Christ, I will accept such a one with open arms and call him "brother." To the best of my knowledge, he is in fellowship with God and should be in fellowship with me, too (cf. I John 1:7).
We must be careful not to go beyond the Scriptures and bind where God has not bound. Likewise, we must be careful not to loose where God has not loosed. I believe the answer above properly respects God's boundaries regarding the submitted question. The primary purpose of baptism is not to make one a member of a local congregation (though such is accomplished); the purpose is to add one to the body of Christ (in the universal sense) where salvation is found. It is possible (though not common) for one to be added to the Lord's church in the universal sense while being associated with a local denomination. We plead with those individuals to come out from among those who fail to worship God in spirit and truth and who do not teach the whole counsel of God (cf. John 4:24; Acts 20:26,27). Being properly baptized for the remission of sins is vitally important, but there is more involved in Christian life than just a proper immersion.
Finally, let me offer some related practical advice to those who have Bible studies with members of denominations, attempting to convert them to Christ (which is a wonderful and ever-challenging endeavor, by the way). It is advisable to get the individual to write down what he or she has done in the past to be "saved" before you ever open your Bible and share what the New Testament teaches about conversion. Why is this a good practice to adopt? Because people will often have some confusion in their own minds regarding their actions of the past, especially after you teach them the truth. It is not uncommon for one to think he has submitted to what the Bible teaches on baptism when he has already shared information with you that proves he has not! It is good to have him write down on paper what he did in the past to be "saved." He might write, for example: "I was saved when I prayed Jesus into my heart on the mourner's bench. Then I was baptized two weeks later." Take his written statement and kindly contrast it to what the New Testament teaches, explaining how he could not have been baptized to have his sins remitted if he believed he was already saved prior to entering the baptistery. He will have an easier time seeing the difference if his own "conversion experience" was clearly detailed and written down first before you begin to teach him the way of the Lord more perfectly. If he is able to see this difference clearly, he will be more likely to respond appropriately and be baptized properly this time.
Thank you for listening, and may the Lord bless you as you strive to do His will.