To determine which statement is incorrect, let's analyze each option based on historical context:

1. The dissatisfaction with British rule intensified in the 1870s and 1880s.
   This statement is correct. During this period, the discontent among Indians grew significantly due to various oppressive policies and economic challenges imposed by the British rule.
2. The Arms Act was passed in 1878, disallowing Indians from possessing arms.
   This is also a correct statement. The Arms Act of 1878 was indeed enacted to restrict the possession of firearms by Indians while allowing Europeans in India liberal access to arms.
3. The Vernacular Press Act was passed in 1880, to support the Government.
   This statement is incorrect. The Vernacular Press Act was actually passed in 1878, not 1880. Its primary aim was to curb the criticism of British policies in the local language press and to exert control over the Indian vernacular newspapers, not to support the government as suggested in the option.
4. In 1883, there was a furore over the attempt by the Government to introduce the Ilbert Bill.
   This statement is correct. The Ilbert Bill controversy of 1883 arose because the proposed bill aimed to allow Indian judges to preside over cases involving British citizens in India, which faced huge opposition from the British community in India.

Therefore, the incorrect statement is: The Vernacular Press Act was passed in 1880, to support the Government.