Learn Dutch: Ik dacht dat de knal van dit rotje half zo luid was als vroeger. - I thought that the bang of this firecracker was half as loud as in the past.

In Dutch, to express "half as [adjective] as", you simply use half zo + adjective + als. While whole-number multipliers require keer or maal (for example, twee keer zo luid als for "twice as loud as"), the fraction half stands on its own without those words.

Because the word dat introduces a subordinate clause, shouldn't the verb was go at the very end of the sentence?

Normally, all verbs in a subordinate clause are pushed to the very end. However, comparison phrases introduced by als or dan (here, als vroeger) are an exception. They are usually placed after the final verb to prevent the sentence from feeling awkwardly bottom-heavy. So, ...half zo luid was als vroeger sounds much more natural to a Dutch speaker than ...half zo luid als vroeger was.

What exactly is a rotje, and why do we say dit rotje instead of deze rotje?

A rotje is a very common Dutch term for a small, cheap firecracker. Because it ends in the diminutive suffix -je, it is automatically a neuter noun (a het-word). Therefore, you must use the neuter demonstrative pronoun dit (meaning "this") instead of deze.