The essential problem is that your inner while <FILEH> loop reads through to the end of the input file, so the outer loop printing "FIRST LINES" only ever executes once. Simply remove this inner read on the filehandle to solve the problem. Indenting the loops helps you see better what is going on.

while (<DATA>) { 
    chomp;

    if (/overlaps/i) {   
         tr/:)(/ /; 
         s/,/ /g; 
         ($xloc,$yloc,$name) = (split)[1,2,7]; 
        print STDERR "FIRST LINES: $xloc $yloc $name\n"; 
    }    

    if (/from/i) {
        s/\(/ /g; 
        s/\)/ /g; 
        s/Pin/ /g; 
        s/at/ /g; 
        s/,/ /g; 
        s/with/ /g; 
        s/bounds/ /g; 
        ($xloca,$yloca) = (split)[1,2]; 
        print STDERR "SECOND LINES: $xloca $yloca\n";
    }
}

__DATA__
Error: Trace to Pin violation on BACK with Clearance (0.3)
Trace (2.97781,39.757),(7.85804,39.757) on Net (GND_SPI) of Size (0.25
+) overlaps
Pin (P101-a4) at (4.05,41.025) on Net (/N$16294) of Size (1.84) (from:
+ Idea/LAYOUT/ROUTE 35) 
P101-a4 4.05 41.025 on Net /N$16294 of Size 1.84 from: Idea/LAYOUT/ROU
+TE 35 

Error: Pin to Fill_Area violation on IN2_GND with Clearance (0.3)
Fill_Area (3.061,-14.425) (379.39,92.965) on Net (GROUND_CHASSIS) over
+laps
Pin (M200-g7) at (235.89,92.046) on Net (/I$13957/N$1243) of Size (1.2
+7). (from: Idea/Util/Fill 07)
M200-g7 235.89 92.046 on Net /I$13957/N$1243 of Size 1.27. from: Idea/
+Util/Fill 07

Error: Fill_Area to Polygon violation on IN2_GND with Clearance (0.38)
Fill_Area (-8.139,-15.475) (92.384,37.151) on Net (GROUND_CHASSIS) ove
+rlaps
Polygon with bounds (6.399,-5.228) (10.0989,-3.178). (from: Idea/Util/
+Fill 34)
Polygon 6.399 -5.228 10.0989 -3.178. from: Idea/Util/Fill 34

Error: Trace to Trace violation on FRONT with Clearance (0.25)
Trace (18.4375,79.2512),(18.7188,78.97) on Net (+3.3V) of Size (0.3) o
+verlaps
Trace (18.169,78.68),(18.169,80.27) on Net (/I$13956/I$68/N$14) of Siz
+e (0.254) (from: Idea/LAYOUT/ROUTE 32)
Trace 18.169 78.68 18.169,80.27  on Net  /I$13956/I$68/N$14  of Size  
+0.254   from: Idea/LAYOUT/ROUTE 32
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