Eating Dairy and Meat at the Same Table
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The rabbis were afraid that if two people eat at the same table and one is eating meat and one is eating milk they might share food and this would lead to someone eating milk and meat together.
- It is forbidden for one person to eat meat and another person to eat dairy at the same table.  This also applies both to poultry and dairy.
- It is forbidden even for one person to eat meat by himself on a table with dairy food on the table or vice versa.
- It is only forbidden for one person to eat meat at the same table as someone eating dairy if both people are familiar with each other. For example, if a person is eating meat at a public table next to someone eating dairy and they don't know one another, it is permitted. 
- If the two people aren't friends and wouldn't take from each other without permission it is still an issue for them to eat together one eating meat and one milk. However, if they aren't friends at all and they wouldn't let the other person take from their food even with permission then it is permitted for them to eat together meat and milk.
- If someone is meat, because he ate meat within the last 6 hours, he can eat parve at the same table as someone else eating dairy because that is too far removed from the original prohibition of meat and milk.
Ways it is Permitted
- If they set an item to remind them not to share food then it is permitted for them to eat together on the same table. This only works for two people sitting together but not for one person eating at a table with food of the other type.
- Similarly, if they eat on separate table clothes or mats that is considered like a reminder.
- Placing a whole loaf of bread that they don’t eat from is considered a reminder.
- The reminder needs to have some height like a pitcher that they usually don’t have on the table or a lantern.
- The reminder should be placed between those eating and not on the side.
- If the people are sitting so far from each other that they can't reach each other's food it is permitted for one to eat meat and one to eat milk at the same table. This solution might not work for one person eating meat at a table where there is dairy or vice versa.
- It is permitted to leave a meat dish and a dairy dish next to one another on a serving table or the kitchen counter, from where people aren't eating. One should still be careful to leave the meat and milk apart so that they don't spill on one another.
- It is permitted to eat at the same table as someone who is eating something which is forbidden, such as non-kosher, except for Chametz or forbidden bread. For example, it is permitted for a Jew to eat meat at the same table that a non-Jew is eating something dairy that is non-kosher.
- It is permitted for one person to eat fish at the same table as someone eating meat. 
- It is permitted for one person to eat fish at the same table as someone eating dairy. 
Parve Foods on the Table at a Meat Meal
- A person should have separate meat and dairy salt containers if he leaves them open on the table and people dip food in because meat and dairy might get into the container and back onto food. However, if it is a covered salt shaker it can be used for meat and dairy, though still some have the practice to have separate salt shakers.
- Bread crumbs left on the table after you ate meat shouldn’t be eaten with dairy and vice versa. However, a large piece of bread left on the table is still parve and you don’t have to be concerned that it was touched by meat or dairy.
- Salads or parve foods on the table during a meat meal if you take with your silverware that you ate with, the food is now meat and shouldn’t be eaten with dairy. However, if they are taken with a serving utensil then one can eat them with a dairy meal unless there’s children at the table who might be not careful not to touch the foods on the table.
- Chullin 104b, Levush 88:1
- Mishna Chullin 103b, Shulchan Aruch YD 88:1. The concern of the Rabbis was that if a person was eating meat at the same table as someone eating dairy, they might come to exchange food and come to eat meat and dairy together. The Levush 88:1 explains that it isn't considered like a double gezerah since it is very common that a person will make a mistake and share food.
- Mishna Chullin 104b, Shulchan Aruch YD 88:1
- Aruch Hashulchan 88:8, Kaf HaChaim 88:13
- Shulchan Aruch YD 88:2, Yalkut Yosef YD 88:7
- Kaf HaChaim 88:9 and 88:15
- Bear Heitiv 88:2 quotes the Bet Yakov who is machmir but the Pri Megadim MZ 88:2 is lenient since it is too far of a gezerah. Kaf Hachaim 88:21 and Badei Hashulchan 88:3 are lenient.
- Tosfot Chullin 104b s.v. keein, Shulchan Aruch YD 88:2
- Kaf Hachaim 88:16, Badei Hashulchan 88:14
- Shulchan Aruch YD 88:2
- Shulchan Aruch and Rama YD 88:1
- Kaf Hachaim 88:26
- Shulchan Aruch 88:2, Badei Hashulchan 88:19
- Gemara Chullin 107b according to the first interpretation of Tosfot s.v. keein. This is codified by the Pri Megadim (Siftei Daat 88:3), Badei Hashulchan 88:15, and Kaf Hachaim 88:10.
- Badei Hashulchan 88:15 isn't sure if the solution of having the food far away works when there is only one person there.
- Shulchan Aruch YD 88:1, Yalkut Yosef YD 88:2
- Kaf Hachaim 88:8
- Shach 88:2, Badei Hashulchan 88:12, Aruch Hashulchan 88:2, Kaf Hachaim 88:3
- Badei Hashulchan (Biurim 88:1 s.v. asur)
- The Shem Chadash (p. 48a) has a doubt whether or not there is a prohibition for two people to eat fish and meat on the same table since there's a danger to eat them together and dangers are treated more severely than something that is forbidden. On the other hand, we can argue that since in order to permit eating the fish after meat or vice versa you just need to wash you're hands we're not concerned that someone would eat them together without washing his hands. He concludes that it is permitted. Kaf HaChaim 173:6 is lenient when two people are eating together but strict when one person is eating with multiple foods on the table. eating fish and meat is dangerous we're not concerned that people will come to eat them together. However, Kaf HaChaim 116:35 is strict even for two people eating at the same table. Yalkut Yosef (YD 87:84, Isur V'heter v. 3, p. 315) rules that it is permitted since it is dangerous we're not concerned that people will eat them together. This approach can also be found in Yabia Omer YD 6:9.
- Yalkut Yosef (YD 87:84, Isur V'heter v. 3, p. 315). Even though some say that it is forbidden to eat fish with dairy based on Bet Yosef 87:3, nonetheless, there is no issue with having two people eating fish and dairy on the same table as the Mishna Chullin 103b explicitly states that it is permitted to eat dairy at the same table that there is fish.
- Rama 88:2, Kaf Hachaim 88:29
- Badei Hashulchan 88:30
- Shulchan Aruch 89:4
- Badei Hashulchan 89:99
- Badei Hashulchan 89:99