• duṣprajasya — whose sons were wicked
  Compound: duḥ (bad) + prajā (offspring). Dhṛtarāṣṭra's defining flaw in the Bhāgavata's eye is not blindness of the eye but of judgment toward his sons.
• alpa-sārasya — whose determination is weak
  Sāra is the inner pith; alpa-sāra is the man with no marrow of resolve. The Bhāgavatam diagnoses Dhṛtarāṣṭra here precisely as the political type Gītā 2.41 calls bahu-śākhā — split, branching, unable to hold one bhakti-anchored intention.
• khala-chanda-anuvartinaḥ — following the desires of mischievous persons
  Khala (rogue, here meaning Karṇa, Śakuni) + chanda (whim) + anuvartin (follower). A devastating compound: the king of the Kurus is reduced to a follower of his own retinue's worst impulses.
• vivitsayā — with the desire of finding out
  Desiderative of √vid (to know). Akrūra's months in Hastināpura are not idleness but jñāna-yajña on Kṛṣṇa's behalf — observing so that the Lord may act with full information.

• Where do you assume you understand a situation after one visit when months of observation are needed?
• What kind of patience does honest scouting require?

Akrūra stays on as a physician who lingers by the bedside not to chat but to read the pulse — the king's weakness, the sons' venom, the courtiers' whispers. Months pass; the diagnosis ripens into something Kṛṣṇa will need to hear plainly.