If your sales improved significantly what challenges you think you're likely to face?

What comes to my mind:

Internally

1. Adjusting production volume (in units for products, in human capacity for services)
2. Meeting high demand customer-service
3. Maintaining high-quality of product, service & customer service in alignment with growth
4. Dealing with work-force demands (more personnel, improvements in work environment, keeping talent)

Externally

1. Dealing with competition as a natural result of success
2. “Adjusting current image to current sales”
3. Maintaining a polished image in the face of reputation damage tactics

According to my opinion, if sales of the product improve significantly then others competitors will be aware of it and announced a new strategy who to compete it and wants to decrease the sale of your product. It would be a big threat for your product. For example Pepsi and Coca Cola they are big competitor for each other’s if one company announced a strategy in market and other will adopt another strategy to capture the market.

quality maintanance

If I can provide the supply required by the increasing demand. Generally, oversale is as bad as undersale.

Depends on the position. If you're a distributor, with main activity in Trading, to fight with the other distributors of your Principal for a larger share

In case you're a producer, to increase production capacity in order to cope with the new challenges, that meaning to allocate enough capital and human resources for it (on a case by case scenario)