If acid gets on your skin, you know immediately because of the burning sensation. This isn't true of bases, which can do their damage unnoticed until you see or smell the results. You'll also know if acid gets into your lungs or eyes, but the pain warning might not provide enough time to prevent serious injury. Be vigilant when working around acid.
Battery room ventilation is critical, but not always properly set up. If you smell "battery fumes," exit immediately. Don't enter again without adequate PPE and/or ventilation.
Battery rooms don't always contain eye washes or showers, yet a portable emergency eye wash kit can easily be provided. If your battery room doesn't have even that minimal protection, correct that right away. Nevertheless, showers and eye washes aren't licenses for carelessness. Acid burns can continue long after the acids are washed off.
Acids aren't always liquids; they also come in granular form. Don't touch granules if you don't know exactly what they are and where they came from.