for the first time 是个介词短语，主要用作状语，表示一个人初次、首次做某事。the first time是个名词词组，除了可以在句子中作名词性成分（如表语、宾语、主语）外，还可以用作复合连词引导时间状语从句。此外，the first time也可以作状语（像其他有些名词词组如today，this week，next month等一样）。the first time作状语有时可以和for the first time互换，但有时它暗示后面还有第二次、第三次等，这是就不宜用for the first time. 以下外COCA语料库the first time作状语的例句：

I remember being in your room the first time and, when I arrived, I sat in a chair, and you were walking around the room from place to place, occasionally stopping to perch on a stool or the couch.

We now have time to get it right the first time.

There's this girl, you didn't quite go about it right the first time, and now you guys are friends. （不宜改用for the first time）

It was lined on three sides by office buildings and stores, and along one side stood the tall, white Congregational church where I'd been married the first time. 不宜改用for the first time。

And if it didn't work the first time, it eventually worked, on the second or fifth or tenth time.  不宜改用for the first time.

We didn't enjoy the book that second time around because, as a result of the lifetime plasticity of our brain, we're literally a different person from the person who read the book the first time.

I nearly voted for Bush the first time, but a series of hilarious misadventures caused me to miss voting. 不宜改用for the first time.

Sir, I'm convinced that you didn't get a fair trial the first time. Well, I can't blame her.  不宜用for the first time.

I didn't know if I'd imagined the different inflection the first time.  不宜用for the first time.

You don't need to be an expert to solve a problem and it doesn't need to be perfect the first time.  不宜用for the first time.

I will admit that before I started taking Wellbutrin the first time I read almost nothing about it.

所以，你认为作状语只能用for the first time的认识是错误的。the first time也是可以作状语的。而且网友的这个句子中用the first time更好，因为它暗示无需第二次，一次就够了。

脏话有很多，所以第一个句子用复数dirty words。一个孩子听见父母说脏话，很可能听见父母说的是一个词如fuck，为什么要用them呢？所以，没有必要改为them。

再次提醒你，阅读英文原文时，不要挑毛病，要尽量去理解说话人为什么这么说。要接受多种不同或类似的表达方式。即使说话人口语中犯一些口误，也不要大惊小怪。你重点理解句子意义。这不是精读教材。