Under けれども, you have the following example sentence:
電車は便利だけれども、いつも人が多い。
Now, since けれども is considered formal, is using だ considered mixing formality levels? According to my understanding so far (I am a beginner), ですけれども sounds more natural。
So, what am I missing?
The だ is only informal in speech.
If it is writing(newspapers, Wikipedia, books etc) it is considered formal.
Also, if you want to make sentence polite, it is enough to use です/ます on the end. What is more, です/ます are in most cases not used in subordinate clauses.
So 電車は便利だけれども、いつも人が多いです。 is enough to make the sentence polite 
電車は便利ですけれども、いつも人が多いです。will sound a bit unnatural. It can be used though, the sentence will sound a bit ungrammatical, and really, really polite. It is something phone marketer can use when trying to show their nice side and make you buy their products etc.
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Do you have a citation for this?
I do understand that asking for a citation might sound at least a bit ungrateful, but, when it comes to something as important as correctly speaking a foreign language… I guess you understand what I mean 
Not a problem, just read this, you will have a deeper understanding since I barely touched the subject here.
http://www.guidetojapanese.org/learn/grammar/polite#_is_NOT_the_same_as
The important thing is that だ is used in many grammatical constructions, you will see in later lessons.
You will also encounter である later on, which is more formal than だ and can be used instead.
And it can appear before some grammar points where だ cannot.
Since I happen to have the Dictionary of Basic Japanese Grammar next to me, do you happen to know if this point is covered there? Also, thanks for the Tae Kim link. I’ll make sure to read it
Nope, だ and です are not covered there, but である is covered in intermediate book on page 31.
Alright, thanks!
Though on page 523 in basic book you have a bit about だ.
And you should read what copula means on wikipedia.
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General guidance is:
です/ます speaking with people you don’t know, people older than you, superiors. Makes sentence polite.
When situation demands, you should use honorific speech/humble speech with superiors, clients etc.
When you are with friends, you use casual speech, including skipping particles lika は、を casual forms of words like けど 、みたい etc。
In writing you use だ orである writing style. It can be mixed together if you want.
Instead of casual words you use written words, so みたい becomes よう,けど becomes けれども or が, について becomes に関して etc.
When it comes to grammar, だ and である are often demanded by some grammar points, while です not. Like in this question, it can be used but it will sound a bit unnatural, overly polite, though it allowed, especially on symposiums, business meetings when someone tries to appeal to bosses/clients.
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