係官『かかりかん』official in charge (n.)
暴言『もうけん』reckless comment (n.)
見逃す『みのがす』to miss, to look, to leave at large (v.)
In this instance, the challenging part for me would certainly be the second line:
Exploring the challenge
Parsing the sentence is the first step I'd undertake.
According to Jisho, the sentence should be parsed this way:
(1): the verb 「見逃す」.
(2): Jisho provides two potential possibilities for わけ, one of which mentions that it's usually written in kana alone:
The other possibility being 分け as in "sharing". Considering that the first reference mentions "usually written in kana alone" and the second one doesn't, it'd be more inclined to go for the first meaning.
The issue here being to make a connection between 見逃す and わけ. This leads me to believe that it verb+わけ might be a construction in Japanese.
訳『わけ』: Coming to a Conclusion
Tae Kim's book mentions the following regarding わけ:
「わけ」is instead used to draw conclusions that anyone might be able to arrive at given certain information. (p.243)
Another possibility is the following, also described in his book:
[...] 「わけ」can also be used as a formal expression for saying that something must or must not be done at all costs. (p.244)
I still wasn't too sure so more research was necessary.
わけにはいかない and its purpose
Looking up 「わけにはいかない」came up with a pleasant surprise at p.581 of DIJG:
"a phrase which is used to indicate that one cannot do something due to an external circumstance".
This would likely fit in the current context all things considered in the sense of:
I can't overlook this reckless comment (from the official in charge).
Thanks for reading!