Insufficient Copper Trace Width/Spacing
Copper spacing is the minimum air gap between any two adjacent copper items. Trace width is the minimum width of a copper item, usually traces (tracks). 

Recommendation:  A minimum of .005” (5 mil) trace width/spacing is necessary. Additional fee is usually charged by manufacturers for trace width/spacing less than .008” (8 mil). All PCB layout packages provide this classical check. Setting sufficient trace width/ spacing in your layout software is the preferred method. Trace width and spacing push and pull against one another, so changing a problem area may require rerouting traces, adding vias, or moving components. 

Insufficient Inner Clearances
Inner clearance is the minimum distance from the edge of a hole to any adjacent, unconnected, inner layer copper. Sufficient inner clearances help ensure that your drill does not cause shorts to your inner copper layers. This is important for both plated and non-plated holes, as non-plated holes may either cut into an adjacent trace or cause shorts during assembly.

Recommendation: A minimum of .012” (12 mil) inner clearance is required and .015” (15 mil) is preferred. Most inner clearance issues can be resolved if negative image inners are provided, but it is preferred to not modify these. Setting these clearances in the layout software, if possible, is the preferred method, as this will maintain intended connectivity. Most layout packages provide this as a DFM check. Those that do not can usually be manipulated to check for this violation by setting spacing and annular ring higher.

Formula: S (spacing) + AR (annular ring) = IC (inner clearance). Another trick that can help resolve problem areas is to move the affected traces to outer copper layers, where this is not an issue.