Challenge Similarity Detector

Java + Jsoup, 1027 bytes

The first two arguments are the question IDs.

Golfed:

import org.jsoup.*;import org.jsoup.nodes.*;class M{String a1[]=new String[100],a2[]=new String[100],c[];int i1=0,i2=0;public static void main(String a[])throws Exception{String r="https://codegolf.stackexchange.com/questions/";M m=new M();m.c=m.a1;m.r(Jsoup.connect(r+a[0]).get());m.c=m.a2;m.r(Jsoup.connect(r+a[1]).get());int s=m.ld(m.a1[1],m.a2[1]);for(int i=2;i<m.a1.length;i++)for(int j=2;j<m.a2.length;i++){if(m.a1[i]==null)break;int d=m.ld(m.a1[i],m.a2[j]);if(d<s)s=d;}System.out.print(s);}void r(Document d){a:for(Element e:d.select("td")){for(Element p:e.select("pre")){ a(p.select("code").get(0).html());continue a;}}}void a(String d){c[c==a1?i1++:i2++]=d;}int ld(String a,String b){a=a.toLowerCase();b=b.toLowerCase();int[]costs=new int[b.length()+1];for(int j=0;j<costs.length;j++)costs[j]=j;for(int i=1;i<=a.length();i++){costs[0]=i;int nw=i-1;for(int j=1;j<=b.length();j++){int cj=Math.min(1+Math.min(costs[j],costs[j-1]),a.charAt(i-1)==b.charAt(j-1)?nw:nw+1);nw=costs[j];costs[j]=cj;}}return costs[b.length()];}}

Readable:

import org.jsoup.*;import org.jsoup.nodes.*;

class M {
    String a1[]=new String[100],a2[]=new String[100],c[];
    int i1=0,i2=0;
    public static void main(String a[])throws Exception{
    String r="https://codegolf.stackexchange.com/questions/";
    M m=new M();

    m.c=m.a1;
    m.r(Jsoup.connect(r+a[0]).get());
    m.c=m.a2;
    m.r(Jsoup.connect(r+a[1]).get());

    int s=m.ld(m.a1[1],m.a2[1]);
    for(int i=2;i<m.a1.length;i++)for(int j=2;j<m.a2.length;i++){if(m.a1[i]==null)break;int d=m.ld(m.a1[i],m.a2[j]);if(d<s)s=d;}
    System.out.print(s);
}

void r(Document d) {
    a:for(Element e:d.select("td")) {for(Element p:e.select("pre")) { 
        a(p.select("code").get(0).html());
        continue a;
    }}
}

void a(String d){c[c==a1?i1++:i2++]=d;}

int ld(String a, String b) {
    a = a.toLowerCase();
    b = b.toLowerCase();
    int [] costs = new int [b.length() + 1];
    for (int j = 0; j < costs.length; j++)costs[j] = j;
    for (int i = 1; i <= a.length(); i++) {
        costs[0] = i;
        int nw = i - 1;
        for (int j = 1; j <= b.length(); j++) {
            int cj = Math.min(1 + Math.min(costs[j], costs[j - 1]), a.charAt(i - 1) == b.charAt(j - 1) ? nw : nw + 1);
            nw = costs[j];
            costs[j] = cj;
        }
    }
    return costs[b.length()];
}

}