If an employee switches employers mid-year, and that employee is covered under 457(B) plans of both employers (who are unrelated), can he/she have two $8,000 deferral limits? It appears that the 457 (B) limits are on a plan-by-plan basis, which would mean that a person could have multiple deferral limits during a year.

Based on the above, if the contribution under the first 457(B) plan was offset by a deferral under a 403(B) plan, will that offset also apply to the limit under the second 457(B) plan? It appears so, because the offset rules are based on what the individual has been able to exclude from income.
Am I missing anything?

Take a look at IRC section 457©. This section discusses individuals who are participants in more than one plan, and limits the aggregate contribution to $7,500 (indexed to $8,000) per year per taxpayer.

Based on this, I would think that the 457/403(B) offsets would be handled on a taxpayer basis each year, regardless of the number of plans under which the taxpayer is covered.

Hope this helps!