"Today" is a noun as well, though. For example: "Today is the day." "Today is a day of rest." In the sentence "Today is Thursday", "Today" is the subject, "is" is the verb, and "Thursday" is the direct object, so it would be a correct sentence technically. Admittedly, it does sound weird without the direct object, so maybe I'm wrong.
Relative to whatever makes up the first place. This can be both a single word, a prepositional phrase or a clause (and the list goes on...), so it's a bit tricky to get right initially, but in this case it's the adverbial "i dag".
For more information, I'd recommend you check out this helpful post on word order written by one of the Swedish mods (1.4 does not apply), and you can also google the "V2 rule".
The verb has to be in the second place in the sentence. In the first place here you have "i dag" so then "er" comes second. If you'd move "i dag" to the end of the sentence, you would write "det er torsdag". So "det" would take the 1st place and, again, the verb "er" would take a 2nd.
It's considered a typo in Bokmål, but would be understood as having the same meaning.
I don't necessarily think it's laziness, but rather them not knowing better. It's one of the more common mistakes to see in writing, and probably has to do with 'i dag' often sounding more like one word when pronounced.
You will see it in older texts as well, and I believe it's still considered correct in Riksmål.