Can dry ice in a liquid poison you?
No it will not poison you to drink a liquid that is directly cooled by dry ice.  At normal pressures there may be some gaseous CO2 dissolved in the liquid giving it a mild carbonation.  However, dry ice can be dangerous to bare skin, mouth, or GI tissue if someone swallows a medium to large pieces of dry ice.  Small pieces are not poisonous, but can produce an unpleasant popping or tingling sensation in the mouth (like extra tingly PopRocks).  In a process similar to making liquid nitrogen ice cream, dry ice can even be used to make ice cream if it is crushed very finely.

Dry ice will sink to the bottom of a drink "cauldron".  If more cooling is needed, do not add regular ice to the cauldron, instead add it to individual drink glasses.

Some simple rules to remember when working with dry ice:


Do not allow dry ice to come in contact with bare skin or other bodily tissue. Keep the dry ice in its packaging at all times. Dry ice has a temperature of -79°C and direct contact can cause freeze burns. If you must handle dry ice, use gloves or newspaper. 
Always handle and store dry ice in well ventilated areas. Carbon dioxide gas is heavier than air. If it is allowed to accumulate in poorly ventilated areas such as boat holds, cellars, cars and vans, it can become a safety hazard, as it will displace oxygen and could lead to asphyxiation. Do not leave coolers in closed vehicles for extended periods and always make sure a window is open. Adequately ventilate areas before entering. 
Do not place dry ice in airtight containers such as stoppered glass jars, bottles or other sealed containers as they could explode. 
Do not store dry ice in refrigerators or freezers. Store in the best insulated cooler possible. 
Do not pack dry ice in direct contact with glass bottles, jars, etc. as the glass could crack and shatter; use non-glass containers. 
If the block is to be reduced in size by breaking or cutting, leave it in the packaging provided to avoid contact with skin and eyes. 
Do not use dry ice in individual drinks. Use only in large punch bowls for effect. Under no circumstances should dry ice be placed in the mouth.


Dry Ice Safety

Dry Ice Safe Handling Practices

MSDS for Dry Ice